AFAICT you can configure TOTP / Security Key based MFA for Twitter and disable text messages, but I don't recall if they force you to give them your phone number first: https://twitter.com/settings/account/login_verification

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.