the most likely reason is the simplest one - he is deliberately manipulating market so that his family’s companies can benefit. He did this very transparently with crypto. Now with a larger stakes.

Corruption plain and simple. Now “lobbyists” will rush in offering him favors so that he removes some restrictions

Yes. It's probably a combination between "have to do something about China; this is something" and "now I can move FX markets at will; time for my friends and I to enrich ourselves"

So he shorted … the market?

Long negative beta securites, short positive betas, on margin. Sell calls on ETFs, buy puts on ETFs, etc. There's risk though because his actions are rather unorthodox and the full effects aren't known (and resulting fear can cause betas to shift drastically)

Or if the necessary capital is out of reach for margin trades or options (for his friends it isn't), buy long 3x inverse ETFs as much as you can risk.

If you expect him to play yo-yo some more, rinse and repeat buying either regular or inverse 3x ETFs as needed.

Is this happening at some scale? Surely. Is it the main purpose? Probably not. I'd expect there are easier ways for corrupt politicians and their cronies to profit.

Yes, you can short a total US market ETF. Or just exit the market and be prepared to enter when the floor is hit (impossible, unless you have outsider knowledge).

If Trump is effectively insider-trading, much of the profit would come from the flip-flopping rumors he spreads every week. To keep going, there does need to be the occasional concrete action, otherwise traders start ignoring the rumors.