Upgrade to Bluetooth5.1?

I recently bought a multi-device keyboard that should allow me to connect both to my DELL PRECISION M4800 laptop and the HP desktop that streams to my television.  Thus, I'd be able to use one keyboard for both devices, instead of needing to swap keyboards when I need to access one or the other.

Problem is, the keyboard uses 3 channels of Bluetooth 5.1 to address three devices.  On the HP that drives the TV, that's no problem, but on my DELL laptop, Bluetooth pairs, and is trusted, but connecting fails.  Since the same version of Solus Linux powers both computers, I'm pretty sure it's a hardware problem.

Does anyone know whether this laptop can be updated to support Bluetooth 5.1?  Can the radio be swapped, or the EFI updated (or both?) to accomplish that?  Or do I need to get another keyboard that uses an older version of BT?

If it's a trivial fix for the DELL, I'd be pleased.  But a keyboard that supports 3 channels of BT3.0 is only $30, so I have a feeling that might turn out to be the answer.