Is it compatible with Aurora DSQL? Or does it rely on Postgres features they do not implement?

Unfortunately, DSQL is still lacking many core Postgres features (most notably foreign keys) that DBOS and DBOSify depend on. DBOS works with most flavors of Postgres though, including regular Aurora/RDS, Cloud SQL, AlloyDB, Supabase, Neon, CockroachDB, and others.