Liverpool's hope is that they definitely want to win when playing with Manchester United because if they win the match, of course Liverpool will get a lot of points and now Arsenal are leading the standings and this is the result of their struggle against Brighton with a score of 2-0.
Setting overly high expectations to win against a weak Manchester United somewhat made Liverpool play a bit hurriedly. The eagerness led to poor handling and passing situations for Liverpool. Even the brightest star, Mohamed Salah, had several misplaced passes, being tightly marked by Luke Shaw, and in the first 45 minutes, he only managed a single shot that couldn't beat Andre Onana.
Whatever the strategy is the fact that Manchester United get one point in this match that's the most important thing in a match, Manchester United Understanding them will not be able to fight Liverpool if they play an open game so they have to find ways to anticipate it.
You're right. Manchester United approached the match as the underdog, opting for a defensive strategy. This defensive stance might be the reason why Liverpool struggled. If Manchester United had approached the game with their familiar attacking style with disjointed midfield, it could have been exploited by the opponent, putting immense pressure on their defense.