Manchester United are already in talks with Erik Ten Hag's representatives over a new contract.
A new deal is expected to be reached soon, with INEOS wanting to give him total trust for the future.
Source: @FabrizioRomano
I think Manchester United does not have any worry about what is going to happen with Ten Hag in the future. He has already brought in a very bad result for Manchester United.
By the way, I cannot trust a coach who has problems with the players in the squad. And it is not one or two players. He has problems with multiple players. Players also have decided to leave Manchester United just because of him. So I do not understand how the Manchester United authority is not concerned about this. Are they keeping him as the coach just because he was able to bring in the FA Cup?

or did they take this decision because they do not have any other better coaches right now?

Yes... It seems that just because he brought the FA Cup twice Manchester United trusts Erik Ten Hag again.

Exactly I have the same thoughts as you where Erik ten Hag often has problems with players so this affects the performance of the players, but Erik Ten Hag has his stance while the players cannot argue with the coach a little, if they argue then it can be removed by Ten Hag.
I don't know,, the news before before Manchester United won the FA was rumored to be a fixed-month decision whether to win or lose Erik Ten Hag would still be fired, but now his contract has been extended again, maybe here we can conclude Manchester United did not find a good coach other than Erik Ten Hag.