I was using Amplitube CS for iPhone on my iPhone 13 and I had the same issue but I have it fixed now by reverting back to 15.6. I'm not sure how long Apple will allow this but here is what I did (I take no responsibility if this messes up your phone. It didn't mess up mine. I was on iOS 16.1.2 when I did these steps on 1/22/2023:
1) I watched this video and I followed the steps with the exception of where to get the IPSW file for iOS 15:
https://www.youtube.com/watch?v=rBOPjjaLy1o
2) I went to this site: iOS Signing Status - iDevice Central to get a signed ipsw download for my iPhone 13 (iOS 15.6 RC was the only signed iOS 15 I could use for my iPhone).
3) I continued on with the steps from the video in step 1.
4) Once my phone restored and backed up, I opened Amplitube and it worked (no fuzzy/sped up audio issues)! The only thing I lost on my iPhone were my phone-saved music files that weren't purchased on Apple Itunes store. That could be because the laptop I used to create the backup for didn't have those original songs on it (on a different PC).
I am okay with having iOS 15.6 RC as I'm not concerned about the new emojis or features of iOS 16.
Again, the ipsw files you use to downgrade the device are determined by Apple to be signed or unsigned and at any time they could unsign it, making it impossible to downgrade to iOS 15. I feel this will be done at some time this year, so the sooner you react, the less likely you'll lose the opportunity.
Cheers to using Amplitube again should you follow this post.