And who knows what happens on that Applecare team when a new product is released. Maybe there was a deluge of Applecare admin requests and they're swamped. They're not robots and they're not perfect. Maybe there was a deeper issue with OP's coverage that needed additional research. And not saying this applies to the OP in any way, but sometimes people just want to rant with no intention of submitting issue feedback to Apple or following through until an issue is resolved. It's OK to give up when it feels like too much effort, but maybe that's when the complaining needs to stop too.
If this was my issue to deal with, I'd be following up regularly and telling the admin team if I don't get a response by xxx date, I will be following up; what's the best way to reach you, if it's not resolved by xxx date, what's the escalation path, etc. That said, I've always had great customer service from the AC admin team, everything from cancelling AC+, to a transfer, and adding an Apple Pencil to my iPad coverage. They've been upbeat, cheerful and highly responsive. But like all customer service relationships, it takes two.