Has a recount ever changed the winner of any major election in US
If you consider a state legislature as "major", then yes, sort of.
Virginia State legislature, 2017. (Decided Jan 2018)
Existing makeup of the body was (D) 49, (R) 51. Democrat governor who would vote in the event of a tie.
My local district.
The initial count was 1 vote in favor of the (D) candidate, Shelly Simonds.
A winning Democrat would have changed the composition to (D) 50 and (R) 50, with a (D) governor voting in the event of a tie.
A recount gave one more vote to the (R), David Yancey. Bringing it to a literal tie at 11,607 votes each.
VA Constitution calls for a random drawing in the event of a tie, so that's what they did. Names printed on slips of paper. Each in a film canister. Both canisters in a bowl...pick one out of the bowl.
The Republican, David Yancey, won. Preserving the makeup of the legislative body, with Republican control.
Had the recount not happened, the Democrat would have won. Giving the Democrats the advantage in the VA State legislature.