There is a big "It Depends" that comes into play.

My DD was starter who pitched a lot of innings. She would not pitch for about 5-6 weeks giving her body a chance to recover. Then she would start back slowly till she was eventually working 4-5 days a week rolling into the fall season.

A pitcher who did not get a lot of innings may be motivated to add another pitch or work all summer trying to improve to get more innings in the upcoming season.

There is no one correct routine for everyone. A pitcher needs to do what they feel is best for them.