I don't think that winning Copa del Rey may change Ancelotti's fate, which has probably already been decided. The team's chemistry is not the same, this year they lost a ton of matches, last year, if I recall correctly, they only lost 2 matches in the whole season. I believe Ancelotti is still a great coach but bringing in Mbappé made things harder for him and he didn't find the right tram balance, just look at Bellingham, he's underperforming a lot compared last year.
First to buttress your points Real Madrid have lost more 10 games this season already, last season they lost just twice so it is a bad season for the club and the manager. The Copa Del Rey and even Laliga trophy wouldn’t been keeping Ancelloti except something like new manager can’t be secured by Real Madrid, this Ancelloti departure isn’t only about the club alone but I see Ancelloti very much interested in the Brazil national team job and doesn’t wants to miss it before the World Cup so he himself wants to go.
As for the players coming in I think fans have actually blamed the wrong man for way too many wrong things which he wasn’t the cause. Ancelotti to me is definitely not the reason for Mbappe coming, Perez has always had an eye for him and he got him, Mbappe isn’t a bad signing either, the club needs time to develop and understand each other before they can be themselves again.
As for Bellingham I don’t understand why people blame Ancelloti too for his poor form, he is currently been played at his main position and he needs to adapt to that. Last season he got goals because he played the false nine position but that isn’t happening now because that position is occupied already and he needs to understand that