I can see that just the 3rd verse would seem confusing, and I was puzzled by this one, as well.
All work (that is, the 39 categories of melacha assigned for Shabbat) are prohibited except for melacha that is necessary for food consumption such as cooking, baking, slaughtering, etc. (I won't delve, here, into the "extension" of the rule such as carrying objects that are not related to food consumption, which is permissible, to an extent.)
The 2nd verse makes this clear.
The 1st verse is clear, also, that food-related melacha is permitted. You cited only part of the verse. Here's the entire verse using Sefaria English translation:
וּבַיּ֤וֹם הָרִאשׁוֹן֙ מִקְרָא־קֹ֔דֶשׁ וּבַיּוֹם֙ הַשְּׁבִיעִ֔י
מִקְרָא־קֹ֖דֶשׁ יִהְיֶ֣ה לָכֶ֑ם כָּל־מְלָאכָה֙ לֹא־יֵעָשֶׂ֣ה בָהֶ֔ם
אַ֚ךְ אֲשֶׁ֣ר יֵאָכֵ֣ל לְכָל־נֶ֔פֶשׁ ה֥וּא לְבַדּ֖וֹ יֵעָשֶׂ֥ה לָכֶֽם׃
And in the first day there shall be to you a holy convocation, and in
the seventh day a holy convocation; no manner of work shall be done in
them, save that which every man must eat, that only may be done by
OK, now to the 3rd verse. You should read Ha'emek Dvavar's explanation that states that the reason for stating just plainly "no work" is only for the purposes of service and offering sacrifices to G-d. I.e. - that you should not be pre-occupied doing melacha that you forget to rest on this day. I'll try to add a link to it, later.