Have look at the link for your shutdown restart issues. I would need some more info though for the power adapter issue. Send me of copy of your IO output please.
Try and redownload my EFI I posted. I've removed my SMBIOS in this one. Use the attached link to run GenSMBIOS and create your own serial, MLB, etc.
You loose Bluetooth due to the USB ports being different on the MacBookPro 13,2 model. You need to remap your USB ports when using a different SMBIOS. Especially on laptops. They seem to be more specific. The USBPorts.kext in my EFI is specific to the MacBookPro 13,3 SMBIOS
Figured I would add my latest EFI. This is running Opencore 0.6.6 on Big Sur 11.1, 4K Display at 60Hz. This EFI is running the Modern UI Opencore icon pack. Currently I use the MacBookPro 13,3 SMBIOS. I don't use HDMI output so I cannot say if it works or not. Besides that everything else is...
This Is one of my later OC EFIs. I don't have my machine handy to give you my latest. This one should boot Big Sur. I am using a Patched EDID in this config. It limits the screen to 48hz instead of 60hz. Latest Whatevergreen has seemed to have fixed this issue though.
Have a look at this thread.
I finally got my 4k display work using this method. It does limit my screen the 48-49hz, but the screen works at full 4k resolution. This EDID patcher was the only way I was...
Finally got Big Sur to run on my Dell 7559. The patched EDID method worked. It allows me to upgrade or Clean install to Big Sur!. Everything works as normal. Thanks so much @Heisenberg68 for bringing this to my attention. Who would have known. Ive run High Sierra, Mojave and Catalina on this...