I think Ten Hag shouldn't be so much in a hurry to get his squad too choked up. He needs to work with the current squad and understand where the limitations lies maybe have a few signing before the season begins, establish a tactics with his starting Xi while the fans and management wait patiently for him to deliver.
I think he doesn't hurry, it is a must to look for new players to improve the squad performance. Man United performance never gets better, it is totally wrong idea if he only needs to focus on the current squad. He needs a few new players to fix the problem in each line of Man United, the current squad isn't competitive enough for the next season. About the tactics, I am very sure that Ten Hag has his own tactics. I believe that targeting some new players is his way to optimize his tactics for Man United.