Earlier quoted context omitted.
I hope they add DNS resolution to the network activity tab.
They can't, because that's handled at the OS level, not the application level. If a browser starts (purposefully) subverting the hosts file or not adhering to resolv addresses, then we've got a bigger problem. Think, a fat client resolving an address differently than a browser; then that's all sort of Pandora's Box.
Related, it should be possible to have “correct” dns in userland that behaves as you describe sans falling back to the system resolver. In my understanding the whole point of DNS over https is to avoid the DHCP assigned DNS address (and of course encrypt)
Finally, I’m pretty sure Firefox at least does its own dns caching. I’ve had to force reload to pick up dns changes already visible to the system resolver.