Your issue is caused by a misconfiguration of your USB map.
The BT chipset is turning off because there's no communication from the motherboard (when it's asleep) even though it is still powered.
You're gonna have to fix that with the following guide (building your own USBports.kext, put it in your EFI kexts folder (/kexts/other for Clover), clean your /L/E from USB related kexts, and rebuild your kext caches.
Important Update: June 2023 From Big Sur 11.3 on the built-in OpenCore XhciPortLimit quirk no-longer worked as described. This became a known "bug", though in reality it was Apple changing their internal code, making a simple "peek and poke" to keep it operating, a difficult task. However, with...
www.tonymacx86.com
Please post your EFI (without SMBIOS serials), and a screenshot of your /Library/Extensions folder