SQLite is written in C. And the most commonly used SQLite driver interfaces to that compiled C code directly via JNI. The PostgreSQL client driver is written in pure Java on the other hand. Has nothing to do with language used. You can wrap anything in a jar (it’s just a zip file).

You could certainly embed PostgreSQL in a jar and you can do something similar to this

https://github.com/electric-sql/pglite

I don’t think there’s that much interest, but it is doable.

EDIT: https://github.com/zonkyio/embedded-postgres