Its been a while since I used Mp3tag. I updated to version 3.05. When trying to move mp3 + cdg pairs mp3tag only moves the mp3. I recall this being one of my most used feature in previous versions. Can you please enable this feature back. If my memory is correct about 2+ year ago in a previous release this feature was disabled and after opening a bug report, it was enabled back on the next release.
Just checked with 3.05a and can't reproduce it.
(As I don't have real cdg files, I just named one like that).
Loaded the MP3 into MP3tag, renamed it with Convert>Tag-Filename and checked in the explorer whether the cdg file also got renamed - and it did.
Then I renamed the cdg file manually (exchanged "better" with "bitter") and renamed the mp3 file - and, as expected, the cdg file stayed as it was and did not get the new name.
The problem is not with the rename function. That works as expected! The problem is with the MOVE function. If you have folder1 with the karaoke files song1.mp3 and song1.cdg. Right clicking on song1.mp3 and moving it to folder2 should also move song1.cdg, but it does not. It only moves the mp3 file and leaves the cdg file behind. For Karaoke files, can you please make the move function also move the corresponding CDG file?