Getting good sound quality on Bluetooth headset seems to depend far more on the Bluetooth profiles used on a connection than the quality of the headset itself.
AAC is quoted in many articles as "the profile you need for Apple devices", and although I found helpful information about finding out the Bluetooth profile used on a given connection, there seems to be no reliable information whether or not AAC really is the only available high-quality audio profile on Apple's mobile OSs.
So, which Bluetooth profiles are available for headphone (stereo audio from device to headphone only) and headset (stereo audio from device to headset, likely mono audio from headset to device, simultaneously) use when used with iOS and iPadOS 14?