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If you're a Postgres pg_search user, partial indexes (https://docs.paradedb.com/search/full-text/index#partial-bm2...) can solve.

If you're creating one Postgres index per user, you're going to have a bad time really fast.

Would eat up inodes? Not sure how these work, does it create separate files for each one?

Index per tenant but yes, if you have hundreds or thousands of tenants that becomes a more difficult problem to manage but not at all unmanageable.