Why doesn't Word work on MacOS Catalina?

Apple is not Microsoft. Contact Microsoft for support with Microsoft products:

Contact a third-party vendor - Apple Support

• Find Microsoft products on Microsoft's website and the App Store.

Please see: 32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support

That fact that it doesn't work after updating says you have Office 2011 or older, or an un-updated copy of Office 2016.

Whether you can install a new copy of Office depends in the SUB-MODEL of the Macbook Pro. Microsoft's current policy is to support only the current and previous two versions of macOS. Today that is Ventura, Monterey, and Big Sur. On Sept 26, that becomes Somona, Ventura, and Monterey.

Find you Macbook Pro SUB-MODEL by doing "About this Mac..." for your Apple menu. Looks like this ::

These articles show Mac sub-models that can run Big Sur, Monterey, and Ventura:

macOS Big Sur is compatible with these computers - Apple Support

macOS Monterey is compatible with these computers - Apple Support

macOS Ventura is compatible with these computers - Apple Support

To run Sonoma, your Macbook Pro's sub-model must be on this list:

Back in 2012 we had to "accept" the bundled apps included with the purchase of a new Mac. If you did not do that back then the opportunity is gone since the only publicly available App Store version requires Ventura or later.

Maybe you could ask Apple if they could please provide a download code for an earlier version that would be compatible with your Mac. Start here: Official Apple Support. The worst they could say is no, but be sure to use those exact words: "download code". They may or may not know what you're talking about, but it's something I know they were able to do in what is now the distant past.

Pages should already be installed on your Mac. In the Mac App store, it should simply have a button that says "Open" rather than "Get".

Catalina is the first MacOS that enforces "all Apps must be 64-bit apps". You did not send Microsoft enough money to get the 64-bit version as well.

If you have old Office keys, here are old Office kits:

https://learn.microsoft.com/en-us/officeupdates/update-history-office-for-mac

One of the three most recent macOS versions is a fairly typical app requirement.

There must surely be a solution other than buying a brand new Mac, but I cannot seem to find it.

If you are unsuccessful in obtaining a Pages version compatible with her Mac, consider using any number of alternatives to Microsoft's never-ending quest to extract your money for the continued privilege of using their bloatware.

For example LibreOffice is free / donationware and is well supported: https://www.libreoffice.org/

There are other, equally good or better alternatives, free or nearly so, but as long as you continue to want Microsoft they will continue to hold you hostage.

See your other post on the same subject.