Not sure which version os MacOS you have upgraded from, but given you have the related article on 32-bit app compatibility, I'm going to guess it was a version pre 10.15 (Catalina), and that your copy of Word is a 32bit bit app.
The bad news it Apple stripped out the 32bit compatibility some time ago before Monterey. So you won't get the existing 32bit version to work. I seem to remember when Apple rolled out Catalina (10.15) they even suggested the unofficial route of having a 'spare' Mac not upgraded so it could continue to run 32bit apps if they could be updated. As a technical guy I used a virtual machine on my Mac to run an old version of the OS and the 32bit apps, but that's not something I would suggest in your case.
I also suspect you purchased your copy of Word/Office outright instead of having a subscription, which means there is no easy way to say this other than you'll need a new version from Microsoft.
Last time I looked trying to get just a copy of Word and not the full Office suite, and it was getting increasingly difficult, as Companies like MS are pushing subscriptions as they like the constant income. If you look on the MS site you should be able to find "Office Home & Student 2021" as a one-time purchase however at about the same cost of a two years of subscription. Academics and others can find various offers if you look real hard, depending on how you qualify.
But I did manage to find a single purchase option for just Word on it's own as an outright purchase; however it is actually more expensive than a one time purchase of "Office Home & Student 2021" (at least in the UK).