That second pasuk, ששת ימים תעשה מלאכה, is a quote from the original commandment about שבת and the משכן:
And when Moshe relays that commandment:
But the question is, what is it doing here? We are talking about יום טוב, not שבת. The commentators offer various explanations.
But there is one answer cited in the name of the Vilna Gaon that I want to focus on. I cannot find the original unfortunately, but it is cited. There are two points about our pasuk: first, the expression שבת שבתון is also used for יום כיפור:
And second, our pasuk calls
this שבת שבתון a מקרא קדש: it is declared holy. The weekly שבת isn’t declared holy; it is inherently holy from שבעת ימי בראשית. Hence in שמות לא:טו it is שבת שבתון קדש לה׳. It is the מועדים that are מקראי קדש. That includes יום כיפור:
The pasuk ends with שבת הוא לה׳ בכל מושבתיכם; in this formulation, that means that each of those seven days are a שבת, a day of ceasing; one of them is a שבת שבתון, a day of more extreme ceasing. And, in fact, the other יומים טובים are called שבת or שבתון.
The Torah borrows the language of שבת and applies it to the מועדים. But they are very different. The Rambam has the law of not working on שבת as both a לא תעשה and an עשה:
And he has the same לא תעשה and עשה for יום טוב:
(and similarly all the other יומים טובים)
There is an explicit commandment of תִּשְׁבֹּת on שבת. On יום טוב, the commandment is מקראי קדש אשר תקראו אתם במועדם. We declare that these days are holy, set aside, to be a מועד, an encounter with הקב״ה. We do that by not doing other things that distract from the מועד. That is the meaning of the שבתון of יום טוב. On שבת, the לא תעשה drives the עשה: we imitate ה׳ by not creating, and therefore we rest from our work. On יום טוב, the עשה drives the לא תעשה: we are occupied with the מקרא קדש and rest from other things, and therefore we do not do work.
Rav Rosensweig has an intricate analysis of the משנה תורה, and notes:
So the Torah opens פרשת המועדים with the statement that ששת ימים תעשה מלאכה: on six of these days, even though they are שבתון, work must be done, the work of creating a מועד. And what is that work?
You are going to eat. A lot.
The unique מצווה of יום טוב, that is not shared with שבת, is שמחה. And we achieve that by eating:
How does stuffing our faces create a מקרא קדש?
Rabbi Shulman likes to point out that the משכן is called the אוהל מועד, the “tent of meeting” or “tent of the encounter”, and that there are two aspects of this encounter: we meet with ה׳ and we meet with the community as a whole. The מועדים, as מקראי קודש, also have to encompass both. When we feast with כנסת ישראל we are encountering הקב״ה. And so ששת ימים תעשה מלאכה, on those six days, there is work to be done; the work of אתה משמח את שלי. We are creating the מועד.