What versions of Pages work with macOS Monterey?

Apple tends to only keep its office software available to users with a machine capable of running the current macOS versions (typically the last 2 or 3). If you have one capable of running that, download Pages on that machine, then go to your Monterey machine and see if it offers and older version for that. Otherwise look for alternative software.

If you have never installed Pages from the Mac App Store in the past, you will not be able to get Pages v13.1 for Monterey now. You will need to use Pages for iCloud, or another word-processing product.

If you have installed Pages for Mac since Oct 2013, then on Monterey, launch the Mac App Store and sign in with the same Apple ID that you used to install Pages previously. Then press cmd+0 (zero) to open the Purchased panel. There will be a Pages icon and probably a blue cloud outline with a down arrow. Click that and you may receive one or more dialogs. Do not click Cancel and the last dialog should ask you if you want to install the last compatible version of Pages for Monterey.

I have not tried this but it is one possible method to get the post-2013 versions of the iWork apps. First, you need access to a computer running macOS Sonoma or Sequoia (as of this date). Perhaps a friend will let you do this. Then you need to sign into the Mac App Store with your Apple ID & "purchase" the apps. Yes, they are free, but the process to acquire them & get them associated with your Apple ID is considered a purchase. You will then need to sign out of the Mac App Store on that Mac (unless it's yours) & delete the apps. Then sign into the Mac App Store on your older Mac & it *might* allow you to download them as I described in my previous reply. 

I have not been able to test this method so it is just a theory but someone posted in the Numbers forum that it does, indeed, work.