So if you have a backup (or not?), you need to start with a clean install and a setting up a new session on Catalina, so:👇🏻
👉🏻 Restart the mac and press up and hold + R to recovery menu,
👉🏻 Go to Disk Utility
https://support.apple.com/en-us/HT208496
👉🏻 At the view menu, select show all devices and select the disk to erase.
👉🏻 Enter a name of the disk such as Macintosh HD and choose APFS and GUID Partition Map.
👉🏻 Click Erase to begin.
👉🏻 Check theses volumes Macintosh HD and Macintosh HD Datas, if it's seems to be OK? Quit the Disk Utility and go to the Catalina Installation.
https://support.apple.com/en-us/HT201314
👉🏻 After that, you need to setting up steps your new user session, not for choosing a backup with Time Machine.
https://support.apple.com/en-us/HT204350
👉🏻 Go to Migration Setup, choose the Time Machine Backup and click to continue.
👉🏻 Select your name, check the content to transfer, and uncheck Apps, Otherfiles and folders and Computer & Network Settings and click to continue to start the transfer.
https://support.apple.com/en-us/HT204350
I hope it's work with the new OS clean for you.
