Sounds like the only release available of pg_background with PostgreSQL 15 is 1.0 though it's not compatible (at least according to https://github.com/vibhorkum/pg_background/issues/43). 1.1 is needed for PostgreSQL 15. Is it possible to get the package for pg_background 1.1 and PostgreSQL 15?
FWIW, 1.2 is available for PostgreSQL 16, and the RPM package has the correct release.