Hey there! Thanks for the input on this. I will try to give you some solutions, but feel free to give me more information so I can properly help you. For example, DuckStation version, console model, burning method and what program did you use for that... All of this is very important.
So, since DuckStation does not work with the .bin/.cue files, what happens when you look at BGM TEST on the Level Select? If it says 00:0D, the tracks are being recognized as they should, but if by any reason there is not a 0D or there is a different hexadecimal number at the end, the tracks are not recognized at all... if this happens, make sure that 1) the .cue and .bin files are on the same directory; 2) that they have the same name; 3) if you have renamed them, the .cue file's contents reflect the new .bin file name as well. Also make sure you are loading the game from the .cue sheet directly and not from the .bin file.
As for burning the project onto a disc... what is the model of your console, and what method did you use? I remember that I once used tools like Brasero which only support burning directly the .bin file, and that might mess up the track table on the CD, since there would be no track information. I would also recommend taking a look at the guide linked on Install Instructions as well; I only use CDRDAO to burn discs because it is the recommended method.
EDIT: Did you notice if sound effects play normally as well?