When you set up CNAME and certain other records in Cloudflare DNS, it defaults to (and heavily discourages you to disable) "proxied" records, which I believe means that the record points to a Cloudflare-owned host which then acts as a reverse proxy to whatever value you'd set. So from the console it looks like you've set the CNAME to a certain value, but in practice it'll be set to a different thing and transparently forward everything via Cloudflare. This is probably where the analytics get inserted, alongside a bunch of other Cloudflare features.

You can disable this, at which point the record will be set as a normal DNS record.

I can see the advantage of Cloudflare's proxy systems, but I wish they'd be clearer about when they're being used and not pretend that this is some DNS feature or that records have been set to one thing when they've actually been set to something else. If nothing else, it makes debugging DNS issues a lot more confusing, particularly if you're not a DNS expert.

If this is HTTPS, how would Cloudfare have the certificate for your domain so that browsers don't warn about a mismatch?

Or is it that when you sign over DNS to a provider, they can take over your cert? They can "ass-cert" their own? :)

I can’t recall if there was a setting to enable reverse proxy, if there was it was On by default since I didn’t expect to have reverse proxy enabled as well. But you can also rp without injecting a script. That’s overdoing it.

I don't know what happened in this situation but beware that CF and similar providers are not true DNS hosting providers. They do DNS, but only so their CDN stuff works, and to lock their customers from using whatever DNS hosting they want. Various things that one might reasonably want to do with your DNS zone are not possible with their product. So use it only because you need to do so in conjunction with their core services.