Hi N Barrett,
Thank you for reaching Microsoft Community.
Thank you for the time and effort spent to troubleshoot the issue. Basing on the steps done, it seems that the issue is on the Surface Laptop 2 and not on the mouse.
Have you tried connecting other Bluetooth device like a keyboard or headset to the device? Do they work or not? This is to isolate if the issue is on the Bluetooth driver or the mouse driver.
Kindly try to run these steps also on your Surface Laptop 2 and see if it has some improvements:
1: Run Surface Diagnostic Toolkit and check Windows Update
2: Update drivers and firmware
Check what is the current OS Build of your Windows version by going to Settings > System > About.
Go to Download driver and firmware for Surface, choose Surface Laptop 2 then click Download on the next page.
Choose the .msi file that matches your current OS Build and click Next.
After downloading, run and install the .msi then Restart.