do I have any responsibility to contact ATF and let them know what is going on?
No. If they actually did complete a F3 and never shipped, that's gonna be on them, having to account for a silencer they transferred on paper but never shipped to the SOT designated on the form.
Either they lost the item and will not admit to it, did not ship it or I'm being taken for a ride here.
They could be playing the foolish game of assigning serial numbers to not-yet-manufactured cans. It's illegal, but it happens.
I'm going to put in a request for charge back on my credit card
That's what I'd do.