Hi BillKane,
Thank you for reaching out Microsoft Community. We're sorry for the delayed response.
To further troubleshoot this issue, what I'd like you to do is to uninstall/reinstall the Bluetooth and Mouse driver in Device Manager.
To do that, make sure that the mouse is currently connected to the Surface device. Open Device Manager. Expand Mouse and Other Pointing Devices**|**Bluetooth. Look for the mouse driver, right-click on each driver and select "uninstall device". Please leave the box unchecked if a pop up will show up before you can uninstall the drivers successfully. Once done, kindly restart your device.
Once it's done completely, go to Settings> Devices and if the mouse is still paired to your device, kindly unpair it and restart the device again, then re-pair it afterwards and check if this works.
If this helps, feel free to mark this post as an answer. Otherwise, don't hesitate to respond to this thread if you need further assistance.
Kind Regards,
Crest_Z