cant locate my system photo library after Big Sur update

Do you remember where you kept your system Photos Library? Have you kept your system photos Library in the Pictures folder or on an external volume? Photos on Big Sur may no longer show the previous System photos Library, if the library is on an unsupported location, for example on an external volume, that has been used for Time Machine backups or an incompatible file system format. If you are keeping he library on an external volume, make sure it has a wired connection (not a network share) and the file system format is MacOS Extended (Journaled) or APFS and not case-sensitive.

How did you do the migration to Big Sur? Usually the files in your home folder will remain untouched, when you install a system upgrade. There is one exception - files and folders that have been stored at the top level of the system volume will be removed by the Big Sur upgrade. If your Photos Library has been stored at the top level of the system volume, not in your user home folder, look at the folder Users > Shared. There may be a folder with "Relocated Items" in the name, where files and folders are collected, that have been removed.

Did you do a Spotlight search for Photos Library? If so, your system library should pop right up.

If not, I suppose that you could create a new system Photos library and download your iCloud photos into it.

-- Rich