I self host Umami. It was a one click deploy from their GitHub Readme. Been using for over a year, more than pleased. It has all the features you’re looking for without GA.

For your purposes, I think all you need is a web server log analyzer. Back in the day, I used Webalyzer to do this. I haven't done any sort of analytics since then, so I don't know what's the best one now. A web search turns up a ton of modern options, though.

Has anyone tried Plausible or Rybbit? Is cookieless important to you or is it a nice to have?