What would be involved, and is it even possible, to set up something like Umami on a site that uses Cloudflare?
Umami specifically it’s impossible at the moment as it requires Node.js, but something similar is definitely possible by using Workers.
There are some services already doing something similar.
Use Logflare and build whatever you want to see with Google Data Studio.
I would highly suggest https://ackee.electerious.com/. It’s pretty easy to setup (assuming you know how to use docker), and you can just set aside one server for Analytics duty for all your applications. It’s cookieless, so you don’t have to do any GDPR banner/popup stuff.
To be clear, it does not run on workers, it runs on a traditional Linux server, but the actual server to client communication script can be loaded in via workers if you want, or you can inline the script, or you can bundle the script in an /assets/ directory on your application (recommended since if it is loaded in through a different sub/domain it will be blocked on most privacy browsers). The script is really small (only ~8kb) designed to run async so it shouldn’t effect loading times much.
I personally use it on my services purely to decide where to spend my time by figuring out the over and under used features, so Ackee being barebones is not an issue (and I would rather respect user privacy by collecting/storing/processing only what is necessary), but if you are very data-driven and need lots of info, something like Matomo might be more what you are looking for.
Thanks everyone for the suggestions. I will follow up.