Hi ELSharipov,
welcome to the Apple (user-to-user) Community.
Re: "bugs with my AirPods pro 2 case"
Resetting the headphones was a good method to try.
Wondering if you have updated the iPhone(s) to the latest iOS version, 16.4.1 (seems that contained bug-fixes) or 16.4.1(a)
That way the firmware on the AirPods could be automatically updated if needed.
If you have updated to the latest iOS version, you could try re-starting the iPhone, which can sometimes restore order: Restart your iPhone
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You might want to check that you are only connecting AirPods to one device at a time. (Eg may not be switching between multiple devices.)
See if turn off / turn on bluetooth helps
or
Switch your AirPods to another device – Apple Support
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Something in this article may help:
Resolve Wi-Fi and Bluetooth issues caused by wireless interference - Apple Support
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How to: Find the serial number of your AirPods – Apple Support
Enter serial number to:
Check Your Service and Support Coverage - Apple Support
or
AirPods Repair & Service - Apple Support
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More support . info. if needed:
AirPods Support Website:
Find all the topics, resources, and contact options you need for your AirPods....
AirPods Support - Official Apple Support
All the best :-)