Just to clarify, what do you mean by "without revealing my personal phone number"?
Did you use a voip number (e.g., Google Voice/Twilio/etc.) instead? Or somehow no number at all? Or a secondary (real) phone number, and Twitter somehow determined it wasn't your primary personal phone number?
Not pushing back against what you said, just trying to understand what factually happened.
It's been years since I tried making a Twitter account, I believe at the time it sometimes required a phone number to sign up but other times it was optional (some A/B test).
I think Bluesky didn't require a phone number to sign up, just an email. Maybe I'm misremembering though and it forced a phone number so I had to provide a fake one or a voip one.
Bluesky didn't require phone numbers back when it was invite only, and then there was a period of time after they allowed everyone to create accounts where users need a phone number to verify. That requirement might have been replaced by a captcha according to:
https://github.com/bluesky-social/social-app/issues/2762
But I didn't try to create an account recently, maybe they went back to requiring phone numbers.