Regardless that still wouldn't protect you against somebody social engineering their support team. The account security page at https://twitter.com/settings/security has an "Additional password protection" but that seems to inhibit automated password reset requests, not support-related ones.
Have you checked: https://twitter.com/settings/apps_and_sessions
It is not unreasonable to assume that this has been changed to the attackers number.
Then, the hacker just gets a local number, which should be easy enough these days.
EDIT: Ah I see elsewhere you said you don't use a smart phone (thus, no authentication app.)
2FA the way Twitter uses it (using SMS to phone number) would in my opinion be less secure rather than more secure because it opens up a whole slew of possible attacks that would then also involve my phone.
Also, I'm not sure how you can say "there is _no way_" your account password was compromised. Can you know for certain that you haven't ever executed code which couldn't potentially be malicious or have security issues? Hell, if you use a web browser there's a non-zero chance that some website you visited was compromised to serve you some javascript which exploits a zero-day in whatever browser you use. You can say that's unlikely, but there's a lot of possible scenarios like that, and you're worryingly willing to just dismiss them all and say there's _no way_ this could be anything other than a vulnerability on Twitter's side.
But: my browser - which I use to access my email - is locked down to the point that a normal user probably wouldn't find it much fun, between umatrix and adblock plus there isn't a whole lot of javascript that runs before I authorize it.
Agreed that it is possible. But still unlikely.
Believing you weren't/couldn't be phished is a great way to get phished again...
Anyway, twitter has had app based 2FA since the end of 2017...
https://techcrunch.com/2017/12/20/twitter-adds-support-for-a...
A year ago, they added security key support:
https://9to5mac.com/2021/06/30/twitter-users-can-now-add-sec...
You don't need a phone to have security.
When I say I'm pretty sure that this machine wasn't compromised that is because I'm utterly paranoid when it comes to stuff like this. Possibly not paranoid enough - given the evidence just obtained...
(don't answer that, just something to think about)
These days, you can never be too paranoid. I religiously 2FA all my accounts the moment I create them.
That's a good one: on a server with an asymmetric encryption system (different decryption key than encryption key) the decryption key is not stored in any automated system, the back up is 'pull' from that one server inbound to this machine.
I guess it is theoretically possible that someone broke into the backup server but it too is locked down pretty good, to the point that if I want access I'll have to get into the car and go there in person. Call me paranoid :)