Is criticizing an expert's qualifications an ad hominem? Particularly when they're using their expertise to argue for an idea as here.

Seems like a double standard. They can use their expertise/reputation to endorse an idea but using that same expertise/reputation to qualify that endorsement is an "ad hominem."

To me discussing their expertise is core to their position, since their whole position is: "I'm an expert, I sign a letter based on my expertise for a specific course of action." If they aren't an expert it cuts right to the core of their position.

Is it though? Is it ad hominem to identify and separate people who know something about a thing from those who don’t?

You raise a good point. When an appeal to authority has already made credentials etc. the issue, challenging that appeal becomes valid. The problem is that OP wasn't just an appeal to authority. It did not open that door. It did make arguments other than identity, and linked to fuller expositions of those arguments. Thus, addressing only identity and ignoring any arguments in either direction remains ad hominem.

It's not ad hominem to separate between experts and non-experts.

Ad hominem is a fair counter-argument to appeal to authority.