Is there a way to see what software is compatible with upgrade to Big Sur?

All 64 bit apps are compatible with Big Sur. If you have an older Mac, open System Information (Applications - Utilities - System Information), click the Software tab on the left and then it will populate with all of your apps. You can then see which are 64 bit and which are 32 bit, if you have 32 bit apps you want to run then either upgrade or replace them prior to installing Big Sur.

As there are many thousands of apps out there that run on Big Sur it is impossible to provide a library of all of them.

There is a third-party site that tracks compatibility issues:

https://roaringapps.com/apps?platform=osx

It relies on user reports so some apps do not have enough reports to be statistically reliable. It also helps to use their "filters" to limit what shows. The default grid can be rather daunting, as it includes Windows and iOS apps.

Hold down the Option key and go to the  menu and select System Information. In the side bar click on Legacy Software and that should give you a list of potential problem apps for Big Sur.