You can try searchIQ. I am using it for a while and my website search looks good so far. Though i am still using free version but they have also released Pro version with added functionality. You can have a look at that also.
Pricing starts at $299/mo. Bit steep if you're a smaller company.
They dropped the free plan some time ago, although if using their WP plugin on a wordpress site, you can still make use of it. I also found SearchIQ but never used it to be honest, so I can't really tell. Algolia is quite powerful too.
Postgresql's tsvectors and GIN, Elasticsearch.
That's on a different layer, though. If you already have your raw content in a database somewhere, you can push that into Elastic or Postgres without too much effort, but if you need to parse your HTML documents first, good luck with that.
Azure Search
(Disclaimer: I am a MSFT employee who works on Azure Search)