> Only Typesense and MeiliSearch properly handled mis-spellings (the "suprman" query).

That's where trigrams come in. pg_trgm can fix mis-spellings, and even compound words ("super man" to "superman"). I opt for performing the search as entered, and use trigrams to offer suggestions to the user, e.g. do the search for "suprman", but show an option to search for "superman".