After I saw that many people uninstalled their mouse drivers, I've also checked my M1 Macbook for any installed ones and I actually found the Logitech Unifying Software that I've installed months ago. These three steps brought the trackpad click on my laptop back:
Remove/Uninstall all third party Wireless Input Device Software like "Logitech Unifying Software"
Go to ~/Library/Preferences (the ~ is important) and remove all plist Files with "trackpad" and "mouse" as part of the filename (e.g. com.apple.AppleMultitouchTrackpad.plist). There should be 5-6 files. Better use the search function.
Reboot (the files will be created again)
After doing this my trackpad was working again. Some functions like "tap to click" that are checked in settings might not work immediately because the state is probably saved in a different plist. So just uncheck and check again to make it function again.
vincely
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