Postgres is smarter about that, too! It evaluates whether the prepared statement is sensitive to parameter changes, and will either use a "generic" plan that's shared across all invocations, or a custom one that is hardwired to the values. There's a setting that controls the behaviour.

https://www.postgresql.org/docs/current/sql-prepare.html

I've not compared the actual behaviour in the codebases I work on, however.