I ran few tests today and my conclusion is that the search function works only with APFS or MacOS extended filesystems. I also performed differents tests with NTFS, FAT or ExtFAT and the search doesn’t find the song with these formatted disk.
So it’s very easy to reproduce the case. For information but I think it is not relevant, my macbook is running Ventura 13.0.1.
the comparison between what Finder can do and what DJay pro can do is not relevant.
In addition, Finder indexes and finds well also files stored in NTFS drives. But I agree with you, by default macOS is readonly limited for NTFS partitions but in my case, I use an additionnal software for enabling full capabilities (read and write).
So, in my perspective, the issues is just located inside DJay pro.