Twitter has a different ‘fuck you pattern’ when you are trying to sign up a new account and they believe you are a spammer. They will force you through never ending captchas that are not meant to verify you, but annoy you until you give up.
I've only gotten a different sort of fuckery, where signup works fine until I follow a single account (or after a few seconds, sometimes) and then I'm banned until I give a phone number.
contacting support used to work after a few days, but not recently.
It’s not just you. Twitter has done this to me, when they assumed I was a spammer. Made me verify extremely difficult captchas that were intended not to verify me but to annoy me so I would give up.
Twitter doesn't do this anymore, probably because they don't want any popup to interrupt users scrolling through more ads, logged in or not.
Instagram and Twitter's login prompt might have been motivated by a desire to increase number of logged in users, and Twitter might have given up on that in recent months considering the increased ad load.