What can I do if the place I was employed at for 9 months randomly stopped scheduling me for 3 weeks for no reason other than that the new scheduling manager apparently didn’t like me?

Unfortunatly, there really isn't much that you can do under the circumstances. In an "at will" employment relationship, an empoyer can set the terms and conditions of employment much as they see fit; this includes who to schedule and when. An employer is under no legal obligation to provide an employee with a set number of hours to work.
The above holds true unless this action violates the terms of an employment contract, union agreement or company policy. Additionally, your treatment cannot have constituted any form of actionable discrimination or retaliation. Unfortunately, merely disliking an employee does not count unless it was due to their race, religion, gender, sexual orientation, age, nationality or disability.

No, you may not sue them for this. It is NOT your employer's job to "provide you with work"--your employer has exactly no obligation in this regard, since employment (unless you have a written employment contract to the contrary) is employment at will. That means you may be terminated, suspended, demoted, have your pay or hours cuts, etc. at any time, for any reason whatsoever, including a manager's personal dislike--just as you would have the right to quit at any time whatsoever, without any notice (providing 2 weeks notice is tradition, but is not legally required), for any reason, including personal dislike. No employer is forced to employ or pay anyone, unless that person has a currently in-force written employment contract.