What version of Big Sur are you running? Click on the Apple menu and About this Mac. Or open Terminal and type "sw_vers".
Sometimes a reboot can help with finding updates.
You can try opening Terminal and typing "softwareupdate --list" to see if there are any listed updates and you can do "softwareupdate --install --all" to install them via Terminal. Sometimes this works better than the graphical Software Update in System Preferences.
If you are on a high security corporate network there may be a problem finding updates. I am trouble-shooting such an issue with my employers corporate network. We think Apple added a CDN via "cdn-apple.com" while we only whitelisted "*.apple.com" which isn't enough. We also think that softwareupdate is looking to validate signatures using a 3rd party Certificate Authority and we may need to whitelist that CA to bypass our packet level inspection proxy. We know that Apple signs firmware updates and that has been an issue due to the CA problem.
You may be able to download a newer version of macOS Big Sur 11.6.4 via the App Store and then run that on top of your older Big Sur version and that will also work. It's just a much larger download and more time consuming to install it.