This is just the fundamental way the internet works, and is the reason that anonymizing proxies like Tor exist.
If you don’t want people to be able to detect your rough geographic location, you should be using a proxy to hide it. For everybody else, knowing the edge server you are closest to is really not a threat.
No, it isn't. This is Cloudflare passing exposing metadata when it really shouldn't. Having a configuration option or a origin response header akin to CloudflareCache: private or something is trivial for them to implement.
The same information would then be available in the timing, but given the distributed nature here, that would be a lot harder to pull off.
There's a real difference between Discord itself knowing your location and any Discord user in the world knowing it. Just like there's a difference between the VPN provider knowing your ipaddr and every website you visit knowing it.
People for whom it's a threat don't necessarily understand anonymizing proxies - very few do. Signal is supposed to provide security for those who do not.