For kiddush on yontif we use two challot. We did not collect manna on Shabbat because of carrying. But carrying is allowed on yontif. Does that mean that manna did not fall on yontif?
Tosefos to Beitza 2b s.v. והיה suggests that whether or not manna fell on Yom Tov is a dispute between conflicting midrashim.
One medrash says:
ויברך ויקדש ברכו במן וקדשו במן שבשבת לא היה יורד מן אבל בי"ט היה יורד
"and He blessed it," "and He sanctified it" - He blessed it with manna and sanctified it with manna, as on Shabbos manna did not come down, but on Yom Tov it came down.
Another medrash says:
שבת לא יהיה (שמות טז) לרבות יום הכפורים לא יהיה בו לרבות י"ט שלא היה יורד בהן מן
"Shabbos it (the manna) will not be" to include Yom HaKippurim. "It will not be on it" to include Yom Tov, on which manna does not come down.
Tosefos (in his first solution) suggests that the Gemara on which he is commenting holds like the second medrash, for reasons which he explains.
As far as to why manna would have not fallen on Yom Tov, despite the permissibility of carrying on Yom Tov for needs of the Yom Tov, Rashi on that Gemara in Beitza understands Rabba to be positing that the significance (חשיבות) of the Yom Tov meals require them to have some degree of preparation and designation from beforehand, and therefore the manna would have to fall beforehand in order to be designated for Yom Tov from before Yom Tov.
My inference from Joshua 5:11-12:
וַיֹּ֨אכְל֜וּ מֵעֲב֥וּר הָאָ֛רֶץ מִמָּֽחֳרַ֥ת הַפֶּ֖סַח מַצּ֣וֹת וְקָל֑וּי בְּעֶ֖צֶם הַיּ֥וֹם הַזֶּֽה׃ וַיִּשְׁבֹּ֨ת הַמָּ֜ן מִֽמָּחֳרָ֗ת בְּאָכְלָם֙ מֵעֲב֣וּר הָאָ֔רֶץ וְלֹא־הָ֥יָה ע֛וֹד לִבְנֵ֥י יִשְׂרָאֵ֖ל מָ֑ן וַיֹּאכְל֗וּ מִתְּבוּאַת֙ אֶ֣רֶץ כְּנַ֔עַן בַּשָּׁנָ֖ה הַהִֽיא׃ (ס)
And they did eat of the produce of the land on the morrow after the passover, unleavened cakes and parched corn, in the selfsame day. And the manna ceased on the morrow, after they had eaten of the produce of the land; neither had the children of Israel manna any more; but they did eat of the fruit of the land of Canaan that year.
It says that the man ceased on the morrow after Pesach which is 16 Nissan, that means that on 15 Nissan, the man still fell!
וַיֹּ֣אמֶר אֲלֵהֶ֗ם ה֚וּא אֲשֶׁ֣ר דִּבֶּ֣ר יְהוָ֔ה שַׁבָּת֧וֹן שַׁבַּת־קֹ֛דֶשׁ לַֽיהוָ֖ה מָחָ֑ר אֵ֣ת אֲשֶׁר־תֹּאפ֞וּ אֵפ֗וּ וְאֵ֤ת אֲשֶֽׁר־תְּבַשְּׁלוּ֙ בַּשֵּׁ֔לוּ וְאֵת֙ כָּל־הָ֣עֹדֵ֔ף הַנִּ֧יחוּ לָכֶ֛ם לְמִשְׁמֶ֖רֶת עַד־הַבֹּֽקֶר׃
And he said unto them: ‘This is that which the LORD hath spoken: To-morrow is a solemn rest, a holy sabbath unto the LORD. Bake that which ye will bake, and seethe that which ye will seethe; and all that remaineth over lay up for you to be kept until the morning.’
Rashbam on Exodus 35:3:1:
לא תבערו אש - לפי שבימים טובים כתיב: אשר יאכל לכל נפש הוא לבדו יעשה לכם ושם הותרה הבערת אש לאפות ולבשל. אבל בשבת כתיב: את אשר תאפו אפו מבעוד יום. ואת אשר תבשלו בשלו לכך מזהיר כי בשבת: לא תבערו אש - למלאכת אוכל נפש וכ"ש שאר מלאכות, שאסורין אפילו ביום טוב.
לא תבערו אש, seeing that in connection with the festivals the Torah wrote that work in connection with the preparation of food was permitted on such days, meaning that the handling of fire was permitted. (Exodus 12.16) Moses had specifically permitted baking and cooking (Exodus 16,23). In view of this the Torah considered it as necessary to repeat the prohibition of handling fire on the Sabbath. If this kind of work was prohibited on the Sabbath, other work which was far less urgent was certainly prohibited also.
So, thinking through a few things, here:
1 - Moshe tells them to prepare food for Shabbat, b/c there would be a double portion on Shabbat.
2 - He also tells them that they can cook (as Rashba"m explains) on Yom Tov, (which could be on a Friday.)
3 - Mahn did not last until the following day, except on Friday to Shabbat.
If they were told to prepare and cook for Shabbat on Friday, how could they do that if there was no man available on Friday, even if it was on a Yom Tov? What would be the point of Moshe pointing out the cooking rules (based on Rashba"m's analysis)?
Related - Beitzah 15b:24-26:
(שמות טז, כג) את אשר תאפו אפו ואת אשר תבשלו בשלו מכאן אמר רבי אלעזר אין אופין אלא על האפוי ואין מבשלין אלא על המבושל מכאן סמכו חכמים לערובי תבשילין מן התורה
Rabbi Elazar said that from this verse, we learn that we may not cook other than from that which was already cooked previously and we cannot bake other than from that which was already baked, previously. From here, we learn the concept of making an Eruv Tavshilin.
(I have to assume that there is no concern that the Eruv would spoil at the time that you make the Eruv. If an Eruv from man was set aside on Thursday eve., it would have spoiled by Friday morning.)