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It's also a crime for people to pretend to be electors and submit fraudulent paperwork.

It's also something that wont be prosecuted under the current admnistration, given a lot of the Trump family have acted in the role of foreign diplomats despite not holding official positions. Prosecuting the states for this would open equal scrutiny for them.

Not in this case, since the US hasn't sanctioned Denmark. Trump's rage bleating on Truth Social doesn't constitute official policy. Now, if restrictions on doing business with Denmark were published in the Federal Register, it could get complicated.

I admit, other than in name, I'm not familiar with the Logan Act. Where does it require sanctions or similar?

There isn't a dispute is there isn't any sort of official government publication about it. Late night rants on Truth Social don't meet that standard.