My suggestion might sound redundant but see if below link helps. I went through same steps and it worked for me. I am also on Catalina.

https://discussions.apple.com/thread/7765052

The Touch ID problem is related to Keychain. 

I went through the following steps (from this Apple Community question) and it worked for me (I am also on Catalina):

1. Open Finder.
2. In the menu bar, click Go once so the dropdown menu appears.
3. Hold down the Option key. You will see a Library folder appear in the list under the Go tab.
4. Open library.
5. Drag Keychains folder into the trash.

You will have to re-enter all keychain passwords, but the Touch ID will work.