how to download catalina and get rid of Big sur?

On an Intel-based Mac: If you use Shift-Option-Command-R during startup, you're offered the macOS that came with your Mac, or the closest version still available.

Alternatively, you can restore from a time machine backup that was made while you used Catalina.

The most common method seems to be restoring from a bootable installer. You would first have to create the bootable installer:

https://support.apple.com/en-ca/HT201372

And then follow the instructions to reinstall macOS onto your Mac from the bootable installer:

1. Reboot your Mac while holding down the Option key to enter the boot selection menu.
2. Select your USB drive from the boot selection menu.
3. Follow the on-screen instructions to format and reinstall macOS on your primary hard drive.

Backup (backup backup backup)

reformat boot disk

Install Catalina from Recovery partition

during setup, when asked if you want to migrate files, point at your backup device

Hope that there were no incompatible file format changes made by Big Sur that would cause a Catalina service to not work correctly