Supabase is an interesting middle ground here — it runs on managed Postgres but gives you access to a curated set of extensions (pg_cron, pgvector, unaccent, PostGIS etc.) without needing to build your own. We used unaccent + GIN indexes for fuzzy city search and it worked well. Still not the same as arbitrary custom extensions, but covers a lot of practical use cases that RDS won't touch.
If I need to do fuzzy location searches, I've thought about just matching geohash locations... even if doing multiple sets and collating them... Note: this was in consideration for something like Scylla or Dynamo.
