Maybe two cohorts. The people we're really sure about, and the ones we're pretty sure about. If they diverge, ask why.
Note that reCAPTCHA thinks you’re a bot if you block analytics…
The Textarea Cache Firefox extension https://addons.mozilla.org/en-US/firefox/addon/textarea-cach... is incredibly useful, but I keep forgetting to install it when I get to a new machine. I forget only once.
If you're running anything with an API, then unless somethings horribly wrong it's even easier: look at the number of requests being made to an API endpoint and spot check a few of the user identifiers (tokens, keys, whatever you're using) to see the variety of users.
All of this is assuming you're trying to merely investigate the volume of use of a feature, not trying to diagnose demographics. If you're trying to extract more fine-grained detail, I don't have as many answers; I hope others will chime in with constructive ways to get things like geographic demographics via server logs.