Here's the process if you have a phone and want to do it fast:
1. Click login on discord on the untrusted device. It shows a qr code next to the credentials box.
2. Log in on phone (which for me is just a faceid check).
3. Scan qr code. Now you're logged in on the untrusted device.
No captcha, no username/password typing on the untrusted device, no second factor even (because your phone is logged in using 2FA so you're using that trust) and definitely no email verification.