Can I play Gust to a Rek'Sai with +2 Assault when he enters the battlefield, or does the Assault get resolved before I can play Gust?

No, you cannot play Gust to remove Rek'Sai, Breacher at the moment he enters the battlefield if he is about to become an attacker, because he gains his Assault bonus passively and immediately upon becoming an attacker.

According to RiftJudge FAQ #1185 and FAQ #2011, Assault is a passive ability, not a triggered ability. Passive abilities do not use the chain and cannot be responded to.

Here is the correct timing sequence for this interaction:

1. Unit Enters: Rek'Sai, Breacher moves to an occupied enemy battlefield.
2. Battlefield Contested: The battlefield becomes contested, and the move ends.
3. Cleanup/Designation: At the end of the move, the game enters a cleanup phase where units are designated as attackers and defenders.
4. Assault Applies: As soon as Rek'Sai, Breacher is designated as an attacker, his Assault passive ability turns on. He immediately gains his Assault bonus.
5. Chain Opportunity: Only after this designation and the resulting passive Assault bonus are applied does the game provide an opportunity for players to play reactions like Gust.

Because the Assault bonus is applied passively at the moment of designation (before any priority window for spells), by the time you have the opportunity to play Gust, Rek'Sai already has his increased Might and would no longer be a legal target if that Might exceeds Gust's targeting requirement.

Note: If Rek'Sai moves to an empty battlefield, he is not designated as an attacker, his Assault remains inactive, and he would remain at his base might of 3, making him a legal target for Gust (as per RiftJudge FAQ #4053 and FAQ #9076).

Note: I could not fully verify the claim regarding a "printed Assault 1" against the retrieved rules.