If Man United has made a lot of improvements I believe their performance will improve but if they keep the existing players like last season I'm not sure Man United will perform well next season (IMO).
You have mad a good point but keeping the players wouldn't necessarily cause them not to getting any better this new season, rather if they resolve the issues on ground a s it has to do with strategies, tactics and coach players relationship, then its very possible they can begin to get some gradual improvement such that before the end of the season, they will be able to have made good results. The teams depth isn't really bad except for their defense line where they have got to make a few changes and try to strengthen it then they can be sure with the right combinations at the Frontline especially the strikers they have a chance to do much better this season.
I don't think keeping the same players of last season will stop Manchester United from improving with their performances because these same players are quality footballers who are obviously not playing at the peak of their strength. I don't know if you noticed how Jadon Sancho improved significantly from what we were seeing at Manchester United immediately he rejoined Borussia Dortmund on loan last season. Personally, I feel Manchester United's problem is majorly tactical and not the players abilities which is why the club can perform better than we've seen in recent years of the club manager Erik ten Hag can introduce a style of football that'll bring out the best from the club players. There's been some additions to the team and I believe they'll improve next season.