It cannot and doesn't have to. That's just for the website to match the e-mail verification request. Once the process is complete, the IP is whitelisted for all subsequent logins to that username from that ip address. Well, unless they also apply more complex rules, like re-prompting for captcha after N failed logins and such.
In that regard it feels a bit like skypeweb, where I've had to log in to the skype website once a month for Miranda to be able to get in.
What's odd is that I have used web discord from this IP successfully previously, even in incognito mode. But when I installed and ran the desktop client (which is just chromium web view pretty much), I got the captcha prompt. So there may be some heuristic shenanigans going on. For example, web discord talks to discord.com/api/v8, whereas miranda talks to the old domain and the old api version discordapp.com/api/v6. It's possible they put in new land mines to discourage people from using old clients, but then again, why would they do that instead of just outright rejecting requests to this old api that's not supposed to be used outside of official discord? (Answer: even the latest mobile iOS/Android Discord app still uses this old domain, possibly the old api too, plus they probably want to support people who are running older versions and cannot update).
As a band-aid, I guess you could modify the message that Miranda shows in response to a captcha challenge. It could state something like "The server requires you to solve a captcha. It is possible you are logging in from a new IP address. Please install the Discord desktop client and complete the first-time login process there.". Or something less wordy. Wish I could narrow down the list of circumstances for you, or figure out why I didn't get prompted from the web version. Maybe I'm just remembering wrong and I did get prompted? Maybe all that needs to be done is to open the web url, like Miranda's been doing? But as I mentioned earlier, that didn't work in my case.
