Which doesn't show the Twitter handle. Anyone can fake this by changing an accounts name, profile picture, bio, and banner.

They can, but reading about Gevers shows a track record. It’s worth being skeptical, but keep his record in mind. Apply the same skepticism to Twitter too, they haven’t got a great record.

It's trivial to change with developer tools, doesn't count as evidence.

This is the only screenshot that the researcher posts as 'evidence' of gaining access to Trump's account. I'm afraid that this one can be easily faked with browser tools. The fact that White house officials have extra security measures on their accounts it is this only screenshot that makes it less convincing that this is true, unless the researcher publishes multiple screenshots or video evidence of logging into the account themselves.

Otherwise it can be easily dismissed as a fake screenshot, even if he 'did it' in the past.

This security researcher uses the Grammarly extension?

Which is trivial to fake by going to your own profile and using your browser's inspector to swap out a few images and change a few text boxes.

I kind of think it's a toss-up if this is true. I can believe Trump would use a very weak password and not apply 2fa, but I'm very surprised that Twitter's additional guard-rails for important accounts didn't prevent this.