Hey Nicholas,
I'm having the same issue as Eric and tried all the steps here. I have a similar PC build, same CPU but my build is an ASUS ROG Strix z590-A Gaming Wifi and Windows 11 Pro, and cannot connect the Xbox Controller Series X (it already has the last firmware) nor any other thing via Bluetooth.
I tried to uninstall and reinstall the bluetooth driver (I have the last available driver from both ASUS and Intel), also tried to install an older version but it always automatically puts me back on the newer version (22.150.0.6), updated the firmware of the controller, updated the BIOS, rebooted various times, updated the intel chipset driver, Windows 11 is up to date, Airplane mode is Off and tried turning it on to see if it was a Gui error, turned bluetooth, wifi and ethernet off, then only bluetooth on, checked windows defender and there's nothing showing that something has been blocked either, turned windows defender off, off and on again, and so on. I work as an IT and am used to debug stuff like that, just spent the last 3-4 hours trying things... nothing makes it work via bluetooth.
The controller and my other devices works when plugged in and the controller can connect to my xbox (and disconnected it from my xbox before trying on windows as I always did in the past while on Windows 10), they worked before upgrading to Windows 11 (when I was on Windows 10), but now none of these can connect via bluetooth anymore. The other devices are a mice, a keyboard, I also tried my magic trackpad, magic mouse and magic keyboard, even random devices I have no clue what they are, truly nothing wants to connect and it's always the same error.
Thanks for any help you guys can provide, at that point I'm going crazy...