Does anyone have any recent experience with making a claim for EC/UK 261 compensation from AA lately? I've just done so for the first time and want to get a better sense of what to expect.

I was supposed to fly AA 141 from LHR-JFK on Sunday evening, 1/5, at 7pm. When I got up that morning, I had an email alerting me that my flight had been canceled and that I'd been rebooked onto another flight (AA 9604) the following morning at 9:50am (which ended up further delayed until a bit after noon). When I called AA's UK number to see about finding an earlier flight (none available), the phone rep said my original flight had been canceled due to an "operational decision." At LHR, the gate staff said the plane that was originally supposed to fly us to NY never made it to London. Given that all other AA flights from LHR-JFK departed and arrived without major issue on 1/5, weather would not be the issue.

After I got home yesterday, I filled out the customer relations form on the AA website and submitted a request for compensation. Within about an hour, I got an email back apologizing profusely for my pain and suffering and promising me 5,000 miles. Given the generic nature of the email and the speed with which it arrived after business hours, I can only assume it was a canned response sent by a bot.

Am I likely to receive a follow-up from AA once they presumably read my email? Will I have to chase them down and escalate to get compensation? Or are they generally good at handling these kinds of claims, and if so, what's the time frame? I'd be very grateful for any recent experiences anyone might have had. I figure I'll give them a couple of weeks to respond to me with an actual human email, and if they don't I'll reach out again.