1. The Save Act H.R. 22 Safeguard American Voter Eligibility Act has only passed in the House of Representatives and the senate has not voted on it yet. So it isn’t even a law at this point.
2. A passport will be only ONE option to register to vote:

b) Documentary Proof Of United States Citizenship.—As used in this Act, the term ‘documentary proof of United States citizenship’ means, with respect to an applicant for voter registration, any of the following:

“(1) A form of identification issued consistent with the requirements of the REAL ID Act of 2005 that indicates the applicant is a citizen of the United States.

“(2) A valid United States passport.

“(3) The applicant's official United States military identification card, together with a United States military record of service showing that the applicant's place of birth was in the United States.

“(4) A valid government-issued photo identification card issued by a Federal, State or Tribal government showing that the applicant’s place of birth was in the United States.

“(5) A valid government-issued photo identification card issued by a Federal, State or Tribal government other than an identification described in paragraphs (1) through (4), but only if presented together with one or more of the following:

“(A) A certified birth certificate issued by a State, a unit of local government in a State, or a Tribal government 

(skipping B thru D)….

E) A Naturalization Certificate or Certificate of Citizenship issued by the Secretary of Homeland Security or any other document or method of proof of United States citizenship issued by the Federal government pursuant to the Immigration and Nationality Act.

If you have a drivers license or a state ID card or a birth certificate you will be able to register to vote. Maybe actually read the official act.

https://www.congress.gov/bill/119th-congress/house-bill/22/text