Equals empty is not same as equals star

For the first, by matching every record, it also matches the empty string. As we can not support left truncation in fulltext, this is the best we can do.

For the second, this is the most common search from the UI, happens every time a search form is displayed, and nothing has been typed in it. Optimizing the jsonb->>'title' ~ '' away allows postgres to use other indexes and make filter queries work faster.

I disagree.
title="*" should match the empty string because the empty string contains zero characters: "A single asterisk (*) is used to mask zero or more characters." B.3.3. http://docs.oasis-open.org/search-ws/searchRetrieve/v1.0/os/part5-cql/searchRetrieve-v1.0-os-part5-cql.html#_Toc324166823

See also https://github.com/folio-org/cql2pgjson-java#matching-undefined-or-empty-values

I have made an optimizing for the way the UI searches with

but that gets applied for title="" as well, which is should not. That query means any record that has a title. In case of title it doesn't matter, as it is a mandatory field, but in general, we need to be able to search for all records that have a publisher, or a language, using this notation.