The FA Cup means a lot to Manchester United and I'm sure the fans value it highly caused by it was also helping them all to be even superior compared to those three clubs at the same time. I believe that all of the United fans are delighted with the result. Despite their struggles in the EPL, United was eventually able to qualify for the Europa League the following season which is good enough rather than got nothing.
United can still compete in the Europa League to replace Chelsea, which has finished behind Tottenham.
Of course, the trophy that MU currently gets is like a special trophy for them. We know that MU has failed to win EPL title for more than a decade. MU won the last FA Cup it has been 8 years ago they won the title, before this season. That why i aggree with you, if the winning match and get trophy over City was a special title for MU, even though they were not getting EPL champions, but preventing City from doubling the domestic title was very important. Because this is also about the derby match, if MU loses again to City, then MU will cause more pain to the fans.
Yes, for other teams, maybe this FA trophy doesn't mean that much, but for Manchester United it will definitely mean a lot to them, after all, with a win, Manchester United can qualify for European competition without having to compete for 6th place in the current standings, they even overtake Chelsea. I don't know whether Manchester United will keep Ten Hag there and still retain the players in the current main squad, in my opinion their victory yesterday was nothing more than luck, the competition next season is certainly very tight and Manchester United must be able to overhaul everything.
If they want to compete in European competitions next season they should be able to prepare their main squad well, at least not make the mistake of buying less productive players, I think Manchester United should be more careful in choosing players before buying them as well as making sure the coach can be better than Ten hag, but I'm still waiting for the latest news about this team, whether they will continue to maintain the current one, if they still maintain it, don't expect to get any trophies next season because the competition is quite tight and will make it difficult for this team to compete.