Is combining a fixed mini drawer with tabs a bad idea?

I'm designing an android app which will have three main categories (e.g. Chores, Rewards) with each 3-4 subcategories (e.g. Today, 7 Days, All). After some experimenting I decided against a bottom navigation since it felt too confusing. Categories will be in a drawer, subcategories in tabs.

However, I'd still like to have the categories always accessible. What do you think about the fixed mini drawer in combination with tabs?

What better solution do you propose?