Had another thought. If you could remote into their server could they not remote into your server?
I'm thinking this could be a good gateway trial option for clients. You set up services on your server and give them limited time access to the server to use the FOSS software. If they want, after the trial they can transfer their data. You then wipe the server to ensure their data is erased.
Also, an option I'm not sure you'd be excited about. You host everything for them and offer the service of using your server for their business needs (rather than just a trial). May be less headache in the long run (less overall hardware means less overall issues, presumably).
For the running of software on your server, I believe there are companies that do that already for the fediverse instances. May be worth looking at and seeing what they offer and for what price.
So looking at "/nodeinfo/2.1" on a couple random servers, they have "localposts", "localcomments", and users: "activemonthly", "activehalfyear", and "total".
Without admin access, someone could get what your asking for, but it would be an overall rather than a current snapshot. If someone wanted to do it, they could daily track the changes in comments, posts, and MAU. From there we could calculate a variety of 'activity' levels for each instance.
I'm semi curious what we'd see, but I don't think curious enough to code a script and run it daily. Maybe if I made a 'server' from an old laptop, but I wouldn't hold my breath on it happening.