If Manchester United faces Ajax, in my opinion, Erik Ten Hag holds the key to the club's weaknesses because he has coached that club before and Erik Ten Hag will definitely prepare an appropriate strategy to beat the Ajax club. However, this could also happen otherwise. Ajax has experienced Erik Ten Hag's coaching system and already understands Ten Hag's characteristics and perhaps this character can be read by the Ajax club so that this could make it easier for Ajax to beat Manchester United. In my opinion, this depends on how Erik Ten Hag handles his club, even so I still support Manchester United compared to Ajax.
What you have described is absolutely what the expectations should be but the challenge will be in if that will later turn out to be the actual reality with Manchester United and Ajax. From the time ten hag left Manchester United till this point, I believe some changes have been made and so he cannot be sure completely if he's still got intact all it takes to easily get ahead of the team, rather he may only try his best and use the little information he's got along side some relativity assumed looking at what applies currently with the team.
Ten Hag has left Ajax since 2022, meaning that Ajax has been trained for 2 seasons by a new coach, so I think there have been many changes that have occurred in Ajax current squad and playing strategy and it will be difficult for Ten Hag to understand with Ajax style of play in the future, especially if Manchester United meets Ajax later, it is very likely that Ajax will have a bigger advantage in the future because most of the players who have been trained by Ten Hag are still playing for Ajax at this tim, of course their certainly still really understand the weaknesses and strengths of Ten Hag game strategy, because I think the style and game of a team will continue to change along with changes in coaches over time, but 80% of the style and strategy of play applied by a coach will remain the same even if he coaches different clubs.
Even though Ajax knew Ten Hag very well and most likely understood how Ten Hag executed his strategy but that didn't immediately give Ajax the upper hand because when two teams fight in the field, what determines is how the two teams play and how big the difference between the two. What I know is that Man United is still stronger than Ajax, especially with the progress they currently have. So if Man United had to play against Ajax, I think it would be an easy win for Man United.