For this coming season, I did not see Manchester United competing with Manchester City. Although Manchester United can make the top four, but the current squad and the coach we have now cannot make us compete favourably with Manchester City.
I like the honesty in your own submission. Whatever will make Manchester United step up to the position of Manchester City in this coming season will take a great grit from the Man U team. Guardiola is still the manager of Manchester City and it doesn't seem like they're willing to perform less than they did were in the last season. Meaning Guardiola will recruit more talented players. Another advantage for Manchester City right now is that they have a manager who's committed to his job and also ready to lead from the front line. He has already understood the club and it's management and knows how to manage them the best.
Yes, Manchester United will definitely find it difficult to really compete with Manchester City next season. Even though Manchester United has currently recruited new players such as Leni Yoro and Joshua Jirkjee, I also believe that Manchester United will still have difficulty competing with Manchester City. Because as we know, Manchester City is a very solid, compact team and has a great coach like Guardiola. The proof is that Manchester City managed to win the Premier League several seasons in a row. So with these facts it is clear that next season Manchester United will have difficulty competing with Manchester City for the top position in the Premier League. However, if they can enter the top 4, maybe Manchester United still has a little hope next season. The reason is that to compete for the top 4 positions, Manchester United only needs to compete with teams like Liverpool, Aston Villa, Tottenham and Chelsea. Even though it is difficult to compete with these teams, in my opinion Manchester United still has hope of occupying 4th place in the Premier League, if Ten Hag and the current Manchester United players play optimally next season.
Talking about players brought in by Manchester City in this transfer market, as far as I know, only one player has been brought in, that player is Savinho. Maybe in this transfer market Manchester City will not bring in many new players, because the current players will certainly still be able to compete quite well next season. So Manchester City will most likely save money in this transfer window.