I don't know for sure about the surface, but many systems use a combined Wi-Fi/Bluetooth device. The Airplane mode effects both radios.
So, if you don't see any Bluetooth indications, even with the View Hidden Devices enabled, do you have the Wireless adapter showing and working?
It seems Device Manager has developed a habit of "forgetting" certain devices. Some say it is because of the Fast Startup configuration but I don't know. I did replace a system SSD the other day and Device Manager never recognized the change. I had to
take extraordinary procedures to get that corrected.
Hopefully, the link provided will correct your situation. But if it doesn't, one thing you might try, if you can, is to turn off the Bluetooth in the Bios and boot normally a few times, then re-enable it.
The link seems to mention the device showing as unknown. If it doesn't show up in some form, it is difficult to install new drivers for it.