Yes, we can say that this is very valuable luck for Ten Hag. In fact, most people predict Man United vs Liverpool will lose, especially if they look at Man United's performance so far, failing in the UCL and also in the EPL, where in fact their position is decreasing. So, Ten Hag is definitely under pressure from the club to make Man United successful again or leave. The transfer market will begin and this is also a significant consideration for Ten Hags to determine the most appropriate and wise purchase/sale given the current conditions. Indeed, there have been several signals about this, perhaps one of which could be quite surprising.
you say the right thing when Liverpool is improving in performance and on the one hand man United is experiencing a draw, which is something amazing because this is like luck and if I look at Ten Hag, he knows that Liverpool is in a very strong condition so they use defensive strategies and midfielders as if become defender who focuses on Liverpool mainstay player.
so every time Liverpool attacks midfielders also try to go the back line to help strengthen defense and one person carrying the ball will be blocked by 2 or 3 players so it will be very difficult for Liverpool players to score and I am actually disappointed because my bet lost first believing at least 1 winning score for Liverpool but it turned out to be only 0-0.
but in long term it looks like Man united will have different performance in EPL because this team has no hope in other competitions so it can maintain its position in EPL to get the best position and lets see in next match whether Man United performance will improve or just will be same.