Congress has no authority, expressed or implied, to take citizenship from people.
Congress has authority to establish a uniform rule of naturalization, and can impose nearly any condition precedent or subsequent.
Bellei lost his citizenship because he failed to comply with a condition subsequent required by naturalization statute.
Incorrect, Article 1 Section 8 clause four specifically enumerates that Congress shall have the exclusive authority over all rules of naturalization. That includes who is a citizen and who is not. Who is a citizen at birth and who is a naturalized citizen. It includes a great deal more and one of those is the AUTOMATIC loss of citizenship.
AND THAT WAS UPHELD BY THE VERY RULING YOU CITE.
Current code in the automatic loss of citizenship is Title 8 section 1481 - (8 U.S. Code § 1481 - Loss of nationality by native-born or naturalized citizen; voluntary action; burden of proof; presumptions)
https://www.law.cornell.edu/uscode/text/8/1481