I've been having the same issue.
I bought my 13" 2018 MacBook Air in December 2018, and this past week, it stopped turning on.
I sent it in for repairs, and they replaced the logic board at a cost of $453. Having seen the articles online about the recall, I contacted support via chat about why it wasn't replaced for free. They just said they were sincerely sorry but did not have a repair program for it. That may be the case, but this is CLEARLY a larger issue than what they suspected in the first limited recall. For comparison's sake, the logic board on my mom's 2010 MacBook didn't fail until after 8 years of use, and my 2009 MacBook Pro still works—it has not yet had any hardware issues aside from a battery replacement. Why is Apple not addressing a problem that should not be happening so early on? After 12 years as an Apple customer, it is really frustrating to watch the quality of products get poorer and to see Apple build an economic model that robs the customer.
Regarding cost, I was told at the Genius Bar that the repair would have been free if my MacBook was covered under AppleCare+, but I doubt it. The details of the AppleCare+ program state that the hardware coverage for a MacBook still costs somewhere between $99-299 plus tax...that's one of the reasons I didn't buy it. Plus, I happened to be living in Korea at the time (but bought the computer at a visit home to the States), and was told that Apple Care would not cover cost at an Apple Store in Korea. Repairs are expensive with or without coverage, and the point is that they should be not happening so soon in the first place.
I am comforted to see that I am not the only one having this issue with the recall, and I am going to continue to make calls to get a refund. I am not sure what my luck will be since they also made replaced the trackpad and the Touch ID button while replacing the logic board—even though I was experiencing NO issues with either the trackpad or Touch ID button whatsoever. They didn't even give any explanation as to why those things were replaced. At this point, I wonder if they did it to pacify me or to avoid having to give me a refund for the logic board...
If my pursuit of the refund works out, I'll post an update.