I don't think there is much wrong with Liverpool's current squad, of course the fans are waiting for a new star player to be added to the squad, maybe it could be because it would be an impressive innovation for the championship. But as you said the current squad is good enough to compete with Manchester City and Arsenal.
They look good currently but pre season games shouldn’t be what you judge a team performance by, we all saw how Chelsea played well in the pre season last season but performed woefully when the league began. Some team don’t perform well in preseason but play well when the season starts. We will see if the squad is good enough compete soon because the premier league is a league you should expect a lot from even with smaller teams they can surprise you. Let’s just hope they maintain their performance and play well when the season starts.
The overall status of the teams cannot be taken into consideration by looking at their performance in the pre-season matches. Because in friendly matches, big teams like City, Madrid, Arsenal and Liverpool form squads with their second row players. And the coach tries to give some experience to the new and young players in his squad. In these matches, no team performs for the sole purpose of winning. So the results of friendly matches are not that important.
Manchester City have lost three out of four friendly matches. Manchester City lost against AC Milan, Barcelona and Celtic. However, the team won the last match against Chelsea by a margin of 4-2. However, I would say that Manchester City are more likely to dominate the Premier League next season. City have a stable squad. Guardiola has backup players even if a player faces injury. And this is very important. Teams like Arsenal and Liverpool are very strong. However, when a key player suffers an injury, their performance drops. But Manchester City is ahead in this aspect.