Supabase's postgres LSP works in a similar way iirc.
Yes, the same way. It's all based on the extremely useful `https://github.com/pganalyze/libpg_query` project, which is where the "extracted the parser from Postgres" part comes in.
Supabase's LSP also uses tree-sitter for corrections and autocomplete, because one drawback of using the server's source is that pg_query only works on well-formed/executable SQL - when it detects a malformed query, it formulates an error and exits, since that's what you want in an SQL server. So for partially-correct syntax and fill-forward, tree-sitter covers the gaps.