I tried for 2 days to install those 3 apps (using my usual Apple ID and password) from the App Store, and they downloaded but would not install. I re-installed Monterey (12.5) - and even restarted in Safe mode - and the apps were still absent, and couldn't be installed from the App Store! After dealing with numerous upgrades to my 2012 Mac Pro, 2009 Mac Pro, iPad Pro, and MacBook Pro, I have NEVER had this problem; Pages, Keynote, and Numbers ALWAYS came with the new OS - I never bothered to back up my applications folder. This must e a new Apple policy, for which there was no warning.
Many problems were documented - even on this support community - about the total loss of people's media files (I have a HUGE set of media files on my iMac) and other problems with Monterey. Several months ago, I upgraded the lap top (to see what I would lose), with no problems and all apps present. Thus, I didn't expect this problem with upgrading my iMac. I'm hoping that, in 4 months, when I trade in this iMac for a Mac Studio computer, the new software will come with ALL the Apple apps, as used to be the case, and that the App Store actually works!