My path was similar. I experienced sudden hearing loss on right side, from perfect hearing, at age 37. The cause was an inner ear infection that damaged the cochlear.
I totally agree that a single sided hearing experience is significantly lacking. No stereo means no orientation to sound, no nuances, hard to track conversation, hard to filter in noise etc. It is a loss of way more than half of the hearing world.
I am a semi-professional singer so I have also been focused on music experiences. I sing solo and in a close harmony group. I continued to sing while deaf for 1 year, but it was very challenging and I relied on lots of feedback from others because it was hard to tell my volume and tone (though pitch was still good.)
I have been a CI user for 1 year now.
EVERYTHING in my life has improved for the better. Conversation, orientation, noisy environments, music.
Music is understandably your main concern. But it is also the most difficult to predict for a precise outcome. No ENT or audiologist will promise you that your previous hearing will be restored, because it just can't be replicated especially for music. However it can get very close.
Many other musicians on this forum can tell you about their music experiences after much longer time than me (which I find very reassuring), I can only talk from 1 year in.
So far the results are great. With my CI and hearing ear combined I have terrific music hearing. I have plenty of nuances and I can sing confidently including in harmony. And I enjoy listening to music as much as before. With my CI alone (when I'm doing rehab practise via my artone) music sounds weird and more electronic but it's improving all the time.
I hope this helps, as well as info you will get from others. There is some great info collected on the music section of the forum.