To the question of "What came first.. Who changed it, and Why?"
Note- the bomberg bible, is a mikraot gedolot, a hebrew bible with commentary. Often translated as "rabbinic bible" in English
The christian chapter divisions came first (though that doesn't include verse enumeration).
Looking back one finds the 1517 bomberg mikraot gedolot uses the christian chapter divisions. The 1525 uses variant which it got from a concordance published by Bomberg, called the Meir Nativ, by Nathan. But he based his concordance on a latin concordance and it seems he didn't seek to deviate from those christian chapter divisions, as his stated reason to have them at all, was to reply to Franciscan Friars that would put arguments to him, so it's possible that that the latin concordance he was working from had that variant in it.
The christian chapter divisions seem to have first been put into the Vulgate, and as wikipedia says the book of malachi has "four chapters in the Latin Vulgate."
The WLC began as a digitized form of the BHS, which is based on(though not identical to), the Leningrad Codex, the WLC then moved towards being a digitization of the WLC away from the BHS ref link here. The Leningrad Codex dates to before there were chapter divisions. The dating of the first edition of the BHS dates to 1968. I see the WLC uses the same chapter divisions as the BHS, which uses the same chapter divisions as the 1525 Bomberg which predates it by far. So the WLC uses the 'jewish chapter divisions'. Looking online, hebrew texts tend to use the WLC and the jewish chapter divisions that it uses, whereas many online english translations will be taking into account the latin vulgate which they use for their chapter divisions.
The earlier I can go back to, for 3 in Malachi, seems to be Bomberg's Mikraot Gedolot printed in 1525. (interestingly the earlier Bomberg uses the christian chapter divisions).
wikipedia on bomberg says "Bomberg was the first to print chapter and verse numbers in a Hebrew bible."
It may be possible to go further back, to a Rabbi Solomon ben Ismael if one had his bible which had the christian chapters written into the margins. But i'm pretty sure that's not online and i've no idea where that is available..but if one saw it then one could check how many chapters he had marked in joel and malachi
"The Christian division into chapters, invented by Archbishop Stephen Langton about the beginning of the thirteenth century, has gained an entrance into the Hebrew Bible. The beginning was made by Rabbi Solomon ben Ismael who first (c. A D. 1330) placed the numerals of these chapters in the margin of the Hebrew text....(Ginsburg)"
The verses weren't numbered yet, the verse division is part of the mesora which has 'sof pasuk'(end of verse) markings / 'full stops', but the numeration of it was later, and seems to have been invented by Nathan as mentioned by this wikipedia article on chapter and verses. He might've used them in his concordance. They were added to the 1548 Bomberg. according to this GM Moore paper on p.76 written by GM Moore referenced by the wikipedia article on the bible's chapter and verses.
Interestingly, while the christian version, the KJV, uses the christian chapters as added to the vulgate.. another fairly christian, or not very jewish, version, the NAB, uses the bomberg style of 4 in Joel 3 in Malachi. Though of course Bomberg wasn't jewish, despite the fact that he was the first to print all tracates of the talmud bavli!
DoubleAA mentions a paper (available on jstor)
The Chapter Divisions in the 1525 Rabbinic Bible
Jordan S. Penkower
It says the christian chapter divisions were added to the 1517 Bomberg rabbinic bible, by editor a Jewish born convert to Christianity Friar Felix Pratensis.
And while I can't see it bring up the chapter difference between Joel and Malachi, it mentions
The 1525 Bomberg Rabbinic bible was edited by Jacob Ben Hayim Ibn Adoniyahu and became the textus receptus.
And it uses different chapter divisions to the 1517 Bomberg Rabbinic bible.
The paper by Jordan notes that the Bomberg 1525 chapter divisions were based on the chapter divisions used in a Concordance called the Meir Nativ by Isaac Nathan. The concordance was written between 1437 and 1447 as mentioned on wikipedia's page on the author Isaac Nathan ben_Kalonymus. The Meir Nativ concordance was published in 1523. The editor of the Meir Nativ was Jacob Ben Hayyim Ibn Adoniyahu (that's the same editor as the editor of the 1525 Bomberg rabbinic bible).
The article by Ram Ben Shalom discusses the concordance, though doesn't mention any difference in chapter divisions from the christian ones (the difference with joel and malachi). But it mentions that the Nathan looked to use the christian chapters and also the christian book order, but worked out the verses based on masoretic markings. He mentions that prior to the publication of the Meir Nativ, chapter divisions appeared as a gloss in the margins of the imola bible 1451, and possibly also done by a few individuals that understood the usefulness of doing so.
Jordan's paper compares the bomberg 1525 with Nathan's concordance, and finds that the chapter numbers are identical. Verses are not marked, and are only done in the 1548 bible(the second printing of the 1525 bible, see p365 of jordan's paper). Jacob Ben Hayyim ibn Adoniyahu wrote an introduction to the rabbinic bible, translated by C.D. Ginsberg. In Jordan's paper he gives a revised translation, and that translation states.
p 361 of jordan's paper translating jacob ben hayyim "....I have adopted the biblical book division........and chapter division used by the author of the concordance [Meir Nativ, Venice, 1523]"
I don't know about the 1517 book order, but the concordance used the vulgate order(pentateuch,historical books, poetry wisdom and prophecy] - vulgate book order has malachi as the last book, and the 1525 used the hebrew "tanach" book order rather than the vulgate book order. So, divrei hayamim(chronicles) as the last book. see p363 of jordan's paper. That order, at least with the prophets at the end is apparently the order that the Septuagint uses.
Jordan's paper verifies that the 1525 does indeed exactly copy the chapters from the concordance.
If and to what extent the 1517 agrees with the vulgate, would be another question. I don't know..
As to where the concordance got their chapters from or whether it was made by the author's team of scholars.. I don't know.
Langton created the christian chapters in 1205(as mentioned by wikipedia's chapter verse page), and the paper by Ram Ben Shalom mentions that they were used in the first latin concordance. Nathan looked here when he created his chapter divisions. And according to the paper by Ram Ben Shalom he intended to follow them, so I don't know why Nathan decided to make one difference. Ram Ben Shalom quotes Nathan who says " I found among their books a book they call in their language Concordantias Bibliae. Its method is that of general roots, bringing together all of the verses of the Holy Scripture in a single table[luah] leaving none out....... I saw that it would not be useful to us to translate it into our Hebrew tongue, owing to the change of the nouns and verbs posited by the translator Jerome..... I preferred to produce it [anew] in our tongue(Hebrew)...And so as not to depart from his method and in order to make it easy to find any verse we seek, in both languages, I have written all of the twenty-four [books of the Bible] according to Christian enumeration of the sections, so that we need not toil to find what we seek therein."
The jewishencyclopedia's article on the word concordance states "The word, in this connection, was first used by Hugo de Sancto Caro (named from Saint-Char, a suburb of Vienne in southern France), who compiled a concordance to the Vulgate about 1244. The revised edition of this work, made by the Franciscan Arlotto di Prato (Arlottus), about 1290, served as a model for the concordance to the Hebrew Bible which Isaac Nathan b. Kalonymus, of Arles in Provence, compiled 1437-45"
There is a wikipedia page on Italian Christian scholar Arlotto. It may have been Arlotto's revised edition that Nathan used as a model for his concordance.
This book titled "The Hebrew Book in Early Modern Italy edited by Joseph R. Hacker, Adam Shear" might mix the words adopted and adapted on at least one point on p257, and may be doing it again but on p257 they say that the concordance chapters were adapted from arlotti's latin concordance of 1290.
So, the 1523 concordance would also have 3 chapters in Joel i.e. as the Bomberg 1525 does. Though it'd be interesting to check the Bomberg 1517, I don't see it online. And Jordan's paper also, mentions a publication used by Christians with a hebrew text that also had the christian chapters, that is the Complutensian Polyglot Bible. (added- according to Jordan the 1517 bomberg has the christian chapters , as in, properly. Not Nathan's joel malachi variant. Nathan's joel malachi variant was introduced to the 1525 bomberg)
The 1517 chapters were not based on the concordance. The earliest source for the chapters of the 1525 is the concordance published in 1523.
As to the why. It looks like down to personal opinion about how many chapters to divide Joel and Malachi into, based on the size of a chapter and whether it's considered to be very much a continuation or not. So the 1525 Bomberg one made 4 chapters out of Malachi, one of the chapters being quite small(As does the JPS and interestingly the NAB does that too). And the Vulgate(or KJV or for a more modern example of the same division, the RSV or NRS) made 4 chapters out of Joel, one of the chapters being quite small. They could have decided to make Joel and Malachi 3 chapters. But still, Ram Ben Shalom's quotation of Nathan indicates Nathan's intention to use the Christian chapters so it's not clear why he seemed to vary them on Joel and Malachi, unless perhaps the latin concordance he used, used that variant.
'Ultimately', as has been pointed out to me, the chapter divisions are late, and the person who divided Malachi into 3 chapters clearly felt that Malachi ch. 3, vv.19-24 are the direct continutation of the previous verses, especially vv.17-18. (similarly, the person who divided Joel into 3 chapters must have felt that what we now call "chapter 4" belongs together, content-wise, with "chapter 3".
A next step could be to look at the concordance by Hugo de Sancto Caro and the revised edition by Arlotto di Prato (Arlottus) 'cos maybe the variant originated there and not with Nathan's concordance.
It's worth bearing in mind that Bomberg was christian, so the chapter divisions that the bomberg 1525 rabbinic bible used weren't 'that jewish', though Nathan was, though nathan might not have made his own variant.
According to https://en.wikipedia.org/wiki/Chapters_and_verses_of_the_Bible#cite_ref-5
"Archbishop Stephen Langton and Cardinal Hugo de Sancto Caro developed different schemas for systematic division of the Bible in the early 13th century. It is the system of Archbishop Langton on which the modern chapter divisions are based "