Answer:
I believe this is false, but there are reasons for it being both
Explanation:
Self-management:
Self-management is our ability to manage our behaviors, thoughts, and emotions in a conscious and productive way. ... Self-management means you understand your personal responsibility in different aspects of your life, and you do what you need to fulfill that responsibility
According to this, self-management is a way to manage all the tasks we have to complete, not necessarily so we can engage in self-care, but so that you get your job done, and with enough time that you are not overwhelmed with work and tasks. Not always so you have extra time.
I hope this helped :D