Pages and Big Sur

The minimum macOS to download Pages is Monterey. If you ever downloaded Pages in the past you can sign in to the App Store with your Apple ID and look in your Account for purchases. If Pages is shown, click on it and you should be prompted to download a compatible version. If you never purchased Pages in the past you're out of luck.

When Apple preinstalls Pages on a Mac, it is the same as your never installing it via the Mac App Store with your Apple ID and you will not be able to obtain that Pages v12.1 compatible version now. Restoring an older version of Pages that was not compatible with Big Sur from a Time Machine backup will not help.

You will need to use Pages for iCloud, iOS, or iPadOS — or choose another word processing application from the many that are available. In the latter case, use Pages for iCloud to export your existing Pages documents as Word documents for forward compatibility.

I am running Big Sur and it came with Pages.

How

Pages v13.2 requires macOS Ventura (13.*) or later as shown in the Mac App Store. This will probably change again with future releases of Pages, Numbers, or Keynote.