Microsoft Surface BT Keyboard Pairing Problem

Windows 11 Version 22H2
I've inherited a Microsoft Bluetooth Keyboard (model 1780) that I can't get to work.
It's a model with no accessible batteries but does have a USB-C port, apparently for charging.
I've tried pairing to my Windows desktop (BT dongle) and a Windows laptop but the KB never shows up in the device list.
Any suggestions?
It's a fine-looking KB and I'd like to pass it on to someone who could use it (or at the very least, keep it as a backup) but first I need to confirm that it's working.
Thanks.

Plug in a USB-C cable and make sure the keyboard is charged.

You could wait a few minutes after plugging it in and while the keyboard is still charging, try pairing it then.

If it pairs, then all is well, let it fully charge and you should be good to go.

Otherwise, you know what to do.

Thanks, Trump81.
I did try that after a Google hint somewhere yesterday. Still no sign of it, though.

In that case, it is possible the battery is kaput and cannot be charged.

You would have to open the keyboard up and replace the battery, which I suspect would be anything but easy.

Just did a quick search and found this, it may be Windows at fault here: