It’s not particularly difficult to setup for full text search backend + API: solr, elasticsearch, typesense, or couchbase are good document oriented solutions that pretty much work out of the box. Postgres or mysql have decent support for full-text search if you’re already on either, though you’ll need to integrate some sort of API layer.

There’s plenty of managed versions of the document oriented too. The biggest issue with Algolia, imo, is they charge per search request. e.g. if you enable autocomplete, every single key press costs you money and they don’t offer a particularly unique product.