What version of Microsoft Word can be used on iMac 2013? -Just updated to Catalina 13.1.3?

No version. Microsoft has dropped support for Catalina because they follow Apple's three-year sliding operating system support model. Microsoft has disabled all Office for Mac license servers for all non-current versions of Micrsoft 365 (subscription) or Office 2019 or 2021 for Mac (single purchase) on macOS Big Sur or later.

Your options for an Office suite compatible with existing MS Office documents is primarily the free LibreOffice Suite, or the purchased/subscribed choice of Softmaker's Office 2021/2024 for Mac suite, also an MS Office clone. Softmaker's solution looks more like contemporary MS Office with native Office document support. The PDF user guide opens from the respective application help menu as a PDF. Probably easier learning curve than LibreOffice in my opinion. Free trial.

As of August 2023, the minimum supported operating system to receive further LibreOffice updates will be Catalina. In my opinion, a year from now, LibreOffice will not support Catalina for product updates, but Softmaker will as the forthcoming Softmaker Office 2024 version supports from Mojave onward.

I think you have to “upgrade” to Microsoft Office 365… you can buy it outright or go for a monthly subscription…. Go here to find out about that : https://www.macworld.com/article/670586/microsoft-office-for-mac-buying-guide.html… you could , of course go for OpenOffice, here: https://www.openoffice.org/ which is free ( but donations welcomed)

john B

The current version of Office and 365 will only install on the three most recent versions of macOS. Today that is Big Sur, Monterey, and Ventura. You cannot install it on any Mac running Catalina which, by the way, is macOS 10.15.

A 2013 iMac can run no higher macOS that 10.14 Catalina.

Older versions of Office may not install because MS has a nasty habit of turning off the activation servers for older version of Office and 365.

There's a Free and Open Source office suite that you can install on your Mac. It can open many Word documents. The latest versions are 7.5.4("early adopter") and 7.4.7 ("tested for longer") – either of which can run on Catalina.

https://www.libreoffice.org/

The developers say that it is a successor to OpenOffice.

See the wiki entry for LibreOffice, where you will find a History graphic of the evolution of OpenOffice and LibreOffice.

Do you have a subscription to Office 365?