I would stick with Twitter. Most widely used emails require a phone number to verify and google voice isn't an option to use. It's likely to be connected.

Alot of people in 2020 disagreed with stuff that businesses required. One side pointed out that they are private businesses and can require whatever they want and that you should just comply.

Same thing could happen with Twitter and I recommend that you not be paranoid and just comply. There's no need to assume the worst is going to happen or that the government is out to get you. The government cares about you and Elon Musk is not going to do anything nefarious. I would accept the new normal of having less privacy and consider it good for society.

I wouldn't worry too much about Twitter requiring the use of an actual name, I think people are overreacting to Elon Musk buying Twitter and making it seem like it's gonna be horrible. Most likely the platform will stay relatively the same and maybe some notable names will be allowed back on.