I kept having this problem with my 6th gen X1 Carbon on Windows 11. I updated the driver from the Lenovo site, completely removed the device and installed it again from official drivers. Regardless, I would frequently have to "troubleshoot" the camera, usually when I need to get online for a telehealth session with a client. Finally, after almost two months of screwing with it, I found my solution: I downgraded to Windows 10.
Go to the Windows 10 media creation tool, download it, and run it when you're ready. Fair warning: this will mean nuking your system, so make sure you have your files backed up to the cloud.