There is no evidence to substantiate what you are saying.

Every possible proof exists already as a possible generation in the grammar of lean or rocq. In no way does that mean we have discovered everything.

Is there a proof that every possible proof is a generation in the grammar of lean or rocq? Sounds like an unsubstantiated claim.

You're confusing the mechanical language of math with math itself.

The map is not the territory, etc. If math was just an elaborate linguistic Glass Bead Game then we wouldn't be funding it. The intuition is that the surface rules of math help uncover the underlying structure of reality.