What techniques are you talking about that cannot be implemented in Postgres?
To be blunt, the intersection of people that know what they are doing on this front and people that choose to use Postgres for this is pretty narrow. It does happen and I've seen a few nice things built with Postgres. But mostly it's just people using the wrong tool for the job.
ParadeDB pg_search bundles Tantivy, a Lucene-inspired library inside Postgres, to give users the feature set (BM25 ranking, tokenizers, faceted search, etc.) while keeping the benefits of Postgres (keep your data normalized, avoid ETL, etc.)
Disclaimer: I work on ParadeDB
Orchestrating this outside of a few Python scripts and a single instance of postgres would have taken much more work!
It took me a while to find it, it looks like they support it via Snowball: https://github.com/snowballstem/snowball
I wish ParadeDB exposed multi-language search capability more prominently in the docs.
https://supabase.com/docs/guides/database/extensions/pgroong...
It looks like at best it makes Postgres aware of more characters
Including but not limited to things that English doesn't have or only has in vestigial forms like grammatical cases, complex word morphology, declensions etc.
That'll be different depending on the language, you can't simply transliterate words to another language, the mapping may change things and the rules might be different.
For example, in English "manage / managers", are practically the same, but transliterating to Spanish can give you "gestionan / gerentes", which diverge very early on.
But yes, most (all?) European languages have vastly more complex morphology than English.