Yup this is exactly the problem, which is why I'm surprised with such decent extension support and heavy use no body has created something that builds better analysis and query pipelines specifically for full text search on top of these databases to solve the relevancy issues.
That's really cool but that's not quite the solution to this problem that I would like.
I haven't used ZomboDB but I have managed plenty of applications where Postgres was the main db and elastic was used for FTS. Zombo looks like it makes it easier to do that type of setup, but Postgres is so high performance (at least at parity on speed w/ Elastic) and Elastic is such a pain in the ass to manage from a DevOps perspective that I'd like to eliminate the need for Elastic by investing some time into Postgres Extensions.
Plenty of great db solutions have come out of Postgres in the last few years based on extensions and fulltext search is one of the areas that has been very quiet, I think we can do better and I'd like to try.
I think in the interim Zombo looks like a really good stopgap though!
Here I'm listing engines based on https://github.com/quickwit-oss/tantivy - tantivy is comparable to Lucene in its scope - but I'm sure there are other engines that could tackle ElasticSearch.
Another thing that could happen is maybe directly embed tantivy in Postgres using an extension, perhaps this could be an option too.