Could you add a poscatboiler category for "definite nouns"?

This is used for Category:Arabic definite nouns. Ideally this should automatically get triggered when using {{definite of}}, or something of that sort (maybe a different {{definite noun of}} would be needed?)

If it's really a category for noun forms, then the entries should probably go in Category:Arabic noun forms instead.

It's not. The entries that go in it are lemma forms that have a definite article in them.