Ah, didn't see the caching part.

Plans for prepared statements are cached though.

Yes if the client manually prepares the statement it will be cached for just that connection because in PG a connection is a process, but it won't survive from one connection to the next even in same process.

Other databases like MSSQL have prepared statements but they are rarely used now days since plan caching based on query text was introduced decades ago.

Only on a per-connection basis