Hmm... this is far outside my domain but apparently there has been no litigation deciding on this yet[].

  While no court has conclusively decided this issue, precedent and the structure of the Constitution dictate that answer is “no.” The availability of an immunity defense arising under federal law does not change which sovereign is prosecuting the offense. The president may not pardon such offenses even when they have been removed to federal court. This stands in sharp contrast to convictions under the Assimilative Crimes Act, 18 U.S.C. § 13, which allows federal courts to incorporate state criminal law to cover acts committed on federal land not otherwise covered by federal law (for example, a domestic assault that takes place on a military base), and which may be pardoned by the president. Those are federal offenses—“against the United States”—because the federal statute borrows the law of the state surrounding the federal enclave, and they are prosecuted by the Justice Department. The charging documents themselves arise under federal law for purposes of Article III.

Your and their argument is compelling, but so is the counter argument IMO. Seems like something that might be tested at some point. If you have any further citations where a court has decided on this would love to look over it.

[] https://www.lawfaremedia.org/article/state-prosecutions-of-f...