I have been a physics professor for almost twenty years, and have written over a hundred journal articles. My best advice is that you are unlikely to derive much value from project planning software. It is designed for supporting projects which are rather different from a single person writing a long research paper (probably for the first time). Dependencies, milestones, critical paths, et cetera are not particularly useful concepts here.

Every discipline has its own style of work, and your faculty mentors and graduate student peers are your best resource for learning that. The work plan you turn in should resemble successful work plans the faculty have seen before- it may be prove helpful, but if not, at least you will have completed the requirement.

There are mac tools you may find helpful, including outliners such as OmniOutliner, writing lools such as Scrivener, and reference managers. Explore, but don't blame yourself if a tool doesn't work well for you. Write every day, and take time every week to reflect on how you are doing. There is no one right way to write, and part of writing a thesis is learning what works for you.