Regarding Erik Ten Hag future with Manchester United, it seems like it will be safe or he will stay with Manchester United for a long time. This season, Erik Ten Hag failed to bring Manchester United to a top 4 finish, which of course was a big failure for Erik Ten Hag this season. But yes, on the one hand, there is no hot issue about Erik Ten Hag dismissal, so I think Manchester United management will still give Erik Ten Hag time next season.
Erik Ten Hag success in bringing Manchester United to the FA Cup trophy is of course an important point in Manchester United management's consideration of him. But currently there are quite a lot of good quality coaches who don't have new teams, such as Xavi, Tuchel and several other coaches. So, if Manchester United is looking for a new coach, they will definitely choose between the two coaches.
I think Ten Hag is being left for the only reason: it turned out to be impossible to find a replacement because there are either weak coaches on the market (like Ten Hag) or those who do not want to work at United. The Cup has nothing to do with this since it is a tertiary title, and in the main competitions United have historical failures: 8th place in the Premier League (with a negative goal difference) and last place in the Champions League group stage. It's sad, but I don't think we can expect anything good from United next season.
In as much as Erik Ten Hang didn't have a nice season, it doesn't make coaches like Xavi Hernandez and Thomas Tuchel better than him. If I am among Manchester United management, I cannot any of the above coaches above Erik Ten Hang.
Certainly, it seems Manchester United is not interested in dismissing their current coach. They might have concluded to give him one more season and make available players for him to try again this season. I personally believe that Erik would have done better if there were available players for him throughout the season. For the majority of the season he played without good defense, to the extent that Casemiro was occasionally made to play defense.