Trackpad gesture for launchpad not working on Monterey on Apple M1 Pro

For troubleshooting try safe mode, see if you have the same issue.

How to use safe mode on your Mac - Apple Support

Note: Safe mode prevents your Mac from loading certain software as it starts up, including login items, system extensions not required by macOS, and fonts not installed by macOS. It also does a basic check of your startup disk, similar to using First Aid in Disk Utility. And it deletes some system caches, including font caches and the kernel cache, which are automatically created again as needed.

Well known problem. Most of us have found that turning bluetooth off and back on will give you back control but keep in mind that you have to do this every time your computer sleeps or you turn it off or restart it. This is the temporary fix for the Monterey OS update till Apple gives us the update that fixes this problem we all are having with our mice, trackpads and other peripheral devices that are affected with that update.

Though, Just FYI, I did read in one forum that this one guy replaced his Magic Mouse and trackpad with new ones from apple and it solved his problem. Just saying, it may be that our old bluetooth equipment may be missing some essential hardware components that make it all work with the Monterey update.

I have the same issue, my go to workaround is to relaunch the dock from activity monitor since the disable/enable bluetooth does not seem to work for me. Let's hope for a fix in the next OS release.