If your Mac is a Late-2014 or newer model, then it is compatible with macOS Big Sur. You can verify your Mac production year from the Apple () menu > About This Mac. Look at the parenthesis on the description line.
If you pass the first paragraph, then you want a last Time Machine backup of Catalina before the upgrade to 11.7.1. It would be wise to first verify if your printer/scanner vendor provides compatible drivers for Big Sur before you upgrade.
Now, you can select the link for Big Sur from How to download macOS - Apple Support using the Safari browser and that Big Sur link will open a Mac App Store window where you can download the full macOS 11.7.1 installer to your Applications folder. Before the upgrade begins, unmount the Time Machine drive and turn off Time Machine in its System Preferences panel.
I do not recommend using the Catalina Time Machine drive with Big Sur, but rather, a new external drive dedicated to Big Sur. You will need to inform System Preferences Time Machine that it is to use the new drive (only). and re-enable Time Machine so that the first full backup of Big Sur occurs after the upgrade has finished.