There are a couple of points I'd disagree here.
1. I don't believe tenfold difference in pricing PostgreSQL vs Redis at fly.io is due to complexity, Postgres is much more complex. If I had to guess at why they priced it that way, I'd say it's because they choose more RAM-beefy machines to host their Redis instances. Other providers may have the pricing completely different.
2. It's been a decade that Lucene-based search engines are no longer the default choice. If for some reason PostresQL's FTS is not the right choice, there are many excellent alternatives like Meilisearch or Typesense.