Can't adjust or turn off bluetooth

Well I'll be ******! I solved it in the most mysterious way. I had previously removed the bluetooth.plist from the library preferences, and restarted the Mac, but with no result. But now when I tried to find the new plist I couldn't find it! Even though I reinstalled the system! But what I did find was a file in that folder that was only called "Bluetooth". So I added ".plist" to the file name and restarted. And now everything is back to normal. Thanks for the suggestions!

Yes they all work fine, but there's one device I want to remove. I've restarted a couple of times, and I even created a new user. When logged in as this new user I still could not change the settings, because this new user's settings were also "configured by a profile".

I'm going crazy if I can't solve this.

This Mac is not connected to any other network than my home LAN. And here's the thing - I did have one profile in the System Preferences>Profiles list, but I removed it. So now there are no more profiles in that place. But I suspect there could be some other more app-connected profile somewhere that's blocking the settings. But I don't know where to look for it. It could be that some code from my old Satechi keyboard needs to be removed, but all pairing/unpairing is done from the keyboard, and it stopped working so there's no solution there either.