>> [the president can pardon] offences under Federal law, but not offenses under State law.> but it is unclear if it holds any legal water.
The claim that POTUS cannot grant clemency for a state conviction definitely holds legal water.
The plain meaning of that clause is extremely clear and its meaning is thoroughly and universally understood in the legal field.
> The reality is that it is legally untested
Re: POTUS directly granting clemency for state convictions, only in a sort of vacuous way. Meaning, this is true for almost everything that is blatantly unconstitutional. E.g., the president having the military disband congress is also "legally untested". I have zero doubt that the current SCOTUS would unanimously reject an attempt by the president to directly grant clemency for a state conviction.
> there's a good chance that Double Jeopardy will protect someone who's pardoned Federally, and then brought up on State charges for the same offense.
Notice that the only reason this indirect argument is made is because POTUS clearly cannot grant clemency directly.
Although this particular theory about Double Jeopardy has not been tested, there's an entire legal doctrine that addresses this question (the Dual Sovereignty Doctrine). The Roberts Court affirmed this doctrine in Gamble.
The primary justification for the Dual Sovereignty Doctrine is that different sovereigns might have different interests. That justification speaks directly to whether the federal executive should be able to grant clemency for state convictions (no, because the state executive might have different interests in prosecution). See https://constitution.congress.gov/browse/essay/amdt5_2_1_2_2...
So,
1. the President very clearly cannot directly grant clemency for state convictions, and
2. the Roberts court affirmed the Dual Sovereignty Doctrine not one year ago in a 7-2 decision. Go read that decision -- the reasons for upholding the Dual Sovereignty Doctrine speak almost directly to the question at hand.
Given these two facts, it's highly improbable that the President could pardon a federal conviction and then convince the Roberts court to extend that clemency to state convictions via a significant narrowing of the Dual Sovereignty Doctrine. In fact, I'd say that a raw exercise of force is more likely to succeed.