I know the title is odd, as Chrome like Firefox just seems to work and work regardless of the Operating system. I have now started to encountered legacy issue with macOS running the latest version of Google Chrome.
My test machine is a 2013 iMac 21.5″ machine that just turned up to the workshop for a fresh build. The first issue was getting Catalina installed after I replaced the mechanical drive with a SSD. Next was finding the correct version of Office 365 for this macOS. Link below
Looking at the internet its hard to find a legacy version from Google. I have found a site that seems to have a link for the installers I don’t know how good it is.
https://google-chrome.en.uptodown.com/mac/versions
I do have a 2013 iMac running MDS server and by shear chance I had downloaded chrome the machine before google cut of the old OS to their default version of Chrome.
I checked the version and you are looking for Catalina Version Version 128.0.6613.138 (Official Build) (x86_64). It also has a nice message telling me macOC 11 (Big Sur) is the oldest version that will work with Chrome.
I have tested the download build from the url and it worked. I also did the app transfer from Mac to Mac and that worked. In short compress the working version of Chrome transfer it across the network to the machine that does not have a working version of Chrome and uncompress, place the app in the Application folder and run the app. After a few moments the app loads up asking you to use Chrome instead of Safari as your default browser (why would I do that.). Anyhow thats it all done and working you even get the not in the about option telling you the OS needs to go to Big Sur to run Chrome.
In short its a bit of a run around to get Chrome working I would look at continue using Safari or download Firefox as of writing this article Firefox was still working on Catalina. You just have to be mindful the macOS version will get to a stage that not much on the internet will work. Fine if the machine is not been setup for that purpose like a build server like MDS.