Also here to confirm that updating to the latest macOS is required! 🖱️👨🏻💻
I ditched updating to Sequoia for a while now (on a 13" M1 MacBook Pro - first gen Apple Silicon)
I broke my old lighting Magic Mouse and bought the new USB-C Magic Mouse as a replacement.
Symptoms that you're experiencing the same situation as I did:
First red flag - the pairing is not Apple smooth.
Second red flag - though the my mouse is black it appeared as a white one in settings.
Third and final - only the pointing worked, all the gestures (including scrolling) were not working.
Apparently is wise to actually read the documentation that comes with the device.
"To use your Magic Mouse and its full range of features, update your Mac to the latest version of macOS"
Apologies for the long answer! I know that mostly anyone frustrating over their mouse not magically pairing right this moment, has got no patience for a long response but I do hope it helps to state the "red flags" of an incorect pairing.
All the best guys!