I confess that this seems like strange advice to me when there are a number of users all reporting the same issue immediately following an update? I mean, I guess it can't hurt to be safe, but doesn't it seem more likely there's been a bug introduced in 11.6.4?
I'd been putting off upgrading to Monterey, but currently that seems like the most promising path forward for me.
Kernel Panics are predominately caused by hardware faults and third-party kernel extensions. There are a few other causes, including some problem in Apple's kexts, but that is rare. If it is hardware, no update will fix it, including upgrading to Monterey. If it is Apple's kext, you have a better chance of making them aware of it through a Genius Bar than sending them reports.
If you think it is the update, use the softwareupdate command in Terminal to download the full installer for the OS version you were using before the update and install that. Create a bootable USB installer and use that to erase your 11.6.4 OS and install the old one.
softwareupdate --fetch-full-installer --full-installer-version 11.6.3
There are full installers for 11.5.2, and 11.6.1, .2, .3, and .4.