And the other day there was a project that allowed to use MS SQL wire protocol on PostgreSQL, so my question is:

Are we just gonna implement everything on top of PostreSQL?

Yes, PostreSQL is like the javascript of databases.

Expect without all the data type issues and Postgresql having a sane design, Postgresql be a pleasure to use and having the courtesy of staying out of my browser.... Please don't tell me that someone compiled Postgresql to WASM.

I don't believe that nobody has ever done this... And google delivers: https://github.com/wasmerio/wasmer-postgres