My sister had this problem that I think got triggered in conjunction with upgrading from Big Sur to Monterey 12.3.1 – trackpad could move the arrow pointer at the login window, but as soon as she logged into her account the trackpad stopped working, only by connecting an external mouse could the arrow pointer be moved. Creating a mew user account and logging into that worked however. So I took a shot at searching for items named “trackpad” in username/Library/Preferences and deleted all .plist files that had “trackpad” in their name. After a restart and log in to her account the trackpad kept working! So it seems at least one of those .plist files was causing the trouble.