Why do I need to verify a phone number to sign up, and can I skip it?
Phone verification is a security measure. Everyone needs a mobile phone when they sign up, and it cannot be turned off, bypassed or switched to email. You do it once when you first sign up, not on every login.
If you do not want to tie your account to your main number, you can verify with another phone and change the number on your account afterwards. Using a temporary number will not lock you out.
If you cannot receive a code when logging back in, use Forgot password on the login page. The reset is done by email and sends you a reset link.
For two factor authentication you can use an authenticator app such as Google Authenticator, which does not need your phone number.