Does the Mac version of Steam install through the Mac App store (or is it offered there), and does that store also have the webview restrictions? If that's the case, I'm wondering if that's triggering them to use web login methods, and while I haven't logged into steam on the desktop again since I installed it on this new one ~6 months ago, I have to log into the website and get a code almost every time I want to do something there, so I wonder if the Mac version of Steam is somehow under the web based login restrictions.

Huh strange. I’ve used steam on windows, Mac and Linux over the years and with different frequencies of use and still only ever have to manually log in once every few months.