I tried to find the specific version that is required for AirPods Pro 2, but Apple.com just said "latest iOS"… Can anyone confirm what is the minimum iOS version that is fully compatible with AirPods Pro 2?
iOS 13 for most functionality
Technically speaking, there is no minimum iOS version as they will function as simple Bluetooth headsets with their functionality limited if the device is non-Apple or a pre-iOS 13 device.
The earliest iPhone supported is the 6s which has a maximum iOS version of 13. Per the technical specifications page, Audio Sharing isn’t supported on iPhone models 6s through 7Plus.
In the fine print on the Technical Specifications page:
AirPods can be used as Bluetooth headphones with Apple devices using earlier software and with non-Apple devices, but functionality is limited
And then in the following point:
Some features require iOS 13 or iPadOS 13 or later, which are not compatible with iPhone 6 Plus, iPhone 6, iPhone 5s, iPod touch (6th generation), iPad Air (1st generation), iPad mini 3, and iPad mini 2.
So, we can extrapolate from this that the limits are hardware related and the minimum iOS version is iOS 13 and a device capable of running that version (or later). To get the Audio Sharing feature, you’ll need iOS 14 or later (and a device that supports it).
iPhone reports AirPods need higher version of iOS
I connected my AirPods Pro 2 to it [iPhone 13], the iPhone warned that certain features needed a higher iOS version.
As for the issue you’re experiencing, there’s no setting or anything user accessible that will modify what gets reported between the accessory (AirPod) and the iPhone. If the iPhone doesn’t correctly detect the AirPod firmware or vice versa, you can start with removing the paring, a restart of the devices and a re-pairing of the AirPods to the iPhone.
I hesitate to tell you to reinstall iOS because you’ll likely undertake this with Apple Support should you decide to open a ticket; I don’t want to make you do this twice. However, if you do decide to go this router, make a backup of your iPhone first!†
To verify that the AirPods are working, you can try pairing them to a different iPhone (running iOS 13+, of course). If they fail there as well, you may have faulty AirPods.
† (IMO) This is likely a bug that is fixed with subsequent versions/updates to iOS that you’re currently using. If you happen to open a support ticket, Apple will likely recommend “update to the latest version.”