They're actually planning on migrating to Postgres in a future release:

>[...] it also opens up new possibilities - not officially yet, but soon - for running Jellyfin backed by "real" database systems like PostgreSQL, providing new options for redundancy, load-balancing, and easier maintenance and administration. The future looks very bright!

https://jellyfin.org/posts/jellyfin-release-10.11.0/

I hope they keep sqlite as a first class citizen.