As for the F35. I don’t get the red harring comment.
It's a red herring because the F-35 was procured beginning in the
1990s,
fifty years after the USAAC was transformed into the USAAF (and longer than that since the USAF becoming independent had become all but inevitable). The same is only slightly less true of the A-10, which was procured beginning in the 1960s, twenty years later. And this was, importantly, after years of evolution of the U.S. air forces that were heavily influenced by heavy bomber and (later) air dominance proponents, and who found the phrase "not a pound for air to ground" to be a sensible sentiment. It's just plain meaningless to discuss those procurements in the context of a continuing USAAC, because achieving that requires so many changes to the development and evolution of the U.S. air forces that those aircraft simply not going to exist in anything like their OTL form. You might as well discuss whether a Britain that wins the American Revolutionary War will still procure the SA80, it makes about as much sense.
You want to discuss what an Air Force (or Air Corps) that, dominated by the army, focuses more on logistics and ground support looks like. That's perfectly reasonable, but the changes here will begin
way earlier than the A-10 program. A continuing USAAC probably means that you have to kill the focus on heavy bombing and an independent Air Force that developed there in the 1930s somehow, but if you do that then U.S. procurement priorities during the Second World War are going to look
a lot different. There's going to be a lot less work on heavy bombers during the 1930s, maybe to the point of not having a B-17 at all (there might be some
prototypes or
experimental aircraft a la the XB-15, but no
production-scale work), and a lot more work on single-engine and two-engine aircraft that can provide close air support or interdiction support. There would be some work on building heavy bombers during the war, if only because the U.S. has few other practical options for hitting the enemy, but that might well end up just being copying British bombers and working on something like the B-29. Doctrinally, the U.S. would be focusing more on fighters and shorter-ranged bombers that are more suitable for supporting army units, so the heavy bomber program would probably be relatively neglected.
You're going to see
even more differences in the post-war era. The early Air Force was laser-focused on two things: fast fighters and jet bombers. Hence the B-47 and B-52, hence the F-86, F-100, in fact the whole Century Series. They did build some aircraft that were more tactical bombing-focused--the F-84, F-84F, and F-105, for instance--and shunted other designs into the role--the F-100--but it was always a secondary priority. Here, those are the top priority, and they probably won't be as obsessed with nuclear delivery as IOTL (or maybe they will be). Fast fighters will certainly also be critical to ensure air superiority for the tactical bombers, but aircraft like the B-47 and B-52 will be distinctly secondary in priority. So instead of the 1950s being something of a wasteland for tactical air, there will be a robust program of development focusing on actually filling the Army's needs instead of doing what the Air Force wants and maybe that's useful for the Army.
By the time the 1970s roll around, the U.S. will have a robust tactical support arm. The A-10 will probably never be procured, because there will not be a crash "oh, wait, conventional tactical air is important" moment with only an obsolescent turboprop aircraft to fill it; rather, it will have been a critical task from the start and there will be existing aircraft that fill all of the niches presented by it (close air support, interdiction, night fighting, day fighting, etc.). Additionally, the Air Force would not have a turf issue with the Army developing fast anti-tank helicopters, since they're one service...at least, not as much of a turf issue. Maybe things will move in a more multirole direction from there--it does seem likely to me--maybe not, but the whole landscape is totally different and the decisions being made are totally different and so this will not have any impact on the Air Force's handling of the A-10 program, much less the F-35 program, since neither will exist ITTL.