Did you backup your data before performing the update?
If not, you probably will want to consider doing that from this point forward.
A good backup plan with cloning software will let you restore the system exactly as it was prior to any update.
While Apple has made some installers available via the Terminal with instructions such as these:
softwareupdate --fetch-full-installer --full-installer-version 11.6.1
You would would only be able to install this on a Catalina system, since the full installer for Big Sur only includes the latest security releases. For Macs released after Big Sur's initial release, only a clone made prior to installing any updates would allow you to restore to prior versions of Big Sur.
No installer can run an older version on top of a newer version.
If you aren't running Ventura, you might want to upgrade to Ventura using one of its earlier releases with the commmand line update suggested above, once you found one that worked.
That's if your software otherwise supports Ventura. Not knowing which OS you are running, it is hard to say what steps would ensure you are functioning again.