This is something I've explored as part of my work on PGlite. It's possible but needs quite a bit of work, and would come with some limitations until Postgres upstream make some changes.
You will need to use an unrolled main loop similar to what we have in PGlite, using the "single user mode" (you likely don't want to fork sub processes like a normal Postgres). The problems come with then trying to run multiple instances in a single process, Postgres makes heavy use of global vars for state (they can as they fork for each session), these would clash if you had multiple instances. There is work happening to possibly make Postgres multi-threaded, this will solve that problem.
The long term ambition of the PGlite project is to create a libpglite, a low level embedded Postgres with a C api, that will enable all this. We quite far off though - happy to have people join the project to help make it happen!
You will need to use an unrolled main loop similar to what we have in PGlite, using the "single user mode" (you likely don't want to fork sub processes like a normal Postgres). The problems come with then trying to run multiple instances in a single process, Postgres makes heavy use of global vars for state (they can as they fork for each session), these would clash if you had multiple instances. There is work happening to possibly make Postgres multi-threaded, this will solve that problem.
The long term ambition of the PGlite project is to create a libpglite, a low level embedded Postgres with a C api, that will enable all this. We quite far off though - happy to have people join the project to help make it happen!