For instance, sitting down once a month on one fitness machine for 5 minutes won't likely yield a benefit ... I'm assuming!
I would push on this assumption a little more.
Consider the general case
If you ask "what's the minimum for me" then your training history is extremely relevant. People's situations vary. They vary so incredibly much that if you ask "what's the minimum in general", for anyone ever, then the answer gets very strange very quickly.
There are plenty of people who are so sedentary that a short walk is a significant effort -- one which probably has a noticeable dose-response effect.
What's the minimum strength training to avoid strength or muscle loss for an elite athlete who just peaked for competition? An absurd amount, probably more in a week than you or I have ever done in a month.
What's the minimum training to gain muscle & strength in someone taking exogenous testosterone? Literally nothing beyond daily life:
Men treated with testosterone who did not work out (T+NoE) gained nearly double the muscle mass as did those who received placebo injections but regularly exercised (NoT+E; 3.2 kg vs 1.9 kg increase).
(From this NEJM paper.)
What's the minimum for someone at the brink of death from starvation, or recovering from a terrible injury? Maybe just eating (even passively) and rest.
The minimum is context-dependent
My point is not that breathing and eating is a good strategy, with or without performance enhancing drugs. It's that the question is meaningless without context. "Who are we talking about?" needs to be answered before we can brainstorm workout minimums. My minimum is not your minimum is not your grandmother's minimum. My minimum today is not my minimum from 20 years ago, or 20 years in the future!
Only once we know who we're talking about and we've established training history and current abilities is it possible to determine likely training minimums.