Looks very interesting. I really like trigram indexes for certain use cases, but those are essentially running an ILIKE %something% on various text content in the DB. So that would fit the described limitations of this index type very well.

Usually you're quickly steered towards fulltext search (tsvector) in Postgres if you want to do something like that. But depending on what kind of search you actually need, trigram indexes can be a better option. If you don't search so much for natural language, but more for specific keywords the stemming in fulltext search can get in the way.

One information that would be nice here is a comparison of the index size on disk for both index types.