upgrading mac Pages version

Once Apple releases a new operating system, the preceding operating system is hidden in the Mac App Store. See How to get old versions of macOS, so you can check your hardware compatibility, and access the older macOS installer. Use Safari on that link, or your results may frustrate you. You can confirm the model year of your Mac from the menu : About This Mac panel.

If you have any Mac that starts up from an Apple Fusion (rotational) drive, I recommend that you think twice about installing Big Sur on that already slow drive. At any rate, Big Sur requires a minimum of 35 GB available storage when upgrading from High Sierra or later, and 45 GB when upgrading from an older operating system.

You don't. Apple does not provide user downloads of full, past Pages installers, and the Mac App Store on Mojave will block you from downloading the current version of Pages in the Mac App Store as it requires Catalina or later.

When I deliberately removed Pages v10.1 from Mojave, knowing that I could recover it from my Time Machine backup, the Mac App Store rightly declined to install Pages v10.2 (Catalina or later), and did not offer to re-install v10.1 again.