How are you supposed to prove the tweet actually happened if you just post a screenshot? It's trivial to forge a screenshot of a tweet to say whatever you want.

You can't prove it happened after twitter deleted it, either.

It's presumably trivial to forge Twitter's "verified" embedding as well, so that doesn't prove anything. (Just have it link to a deleted tweet - plausible deniability!)

If it still exists, just add a link to it underneath the screenshot. If it was deleted, then there's not much you can do, but that's no different than if you had embedded it.

You search it. If it is deleted, you move on with your life and stop worrying about the past.