I am changing from OS Catalina to macOS Big Sur. Do I need to back everything up?

Yes, backing up is typically the very first step BEFORE performing a macOS update ... even for minor updates.

In addition, your backup strategy should have, as a minimum, two methods:

1. Perform a manual Time Machine backup.
2. Using a third party backup solution, like Carbon Copy Cloner, make a complete clone of your Mac's system drive. The reason for this step is to make restoring your Mac simpler should the system drive fail and it has to be replaced.

In reality you should always have a full backup available.

Time Machine is a simple app that does it in the background.

All you need is an external drive plug it in, open Time Machine

in System Preferences, select the drive then start.

BTW, trusting your digital life to a single device is an accident

waiting to happen.

Yes; you may encounter trouble or wish to downgrade. In addition, drives may fail at any time, not just during an upgrade.

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