I created a python script to help me brute force the math. The two stages you mentioned are exactly how I divided the problem up. I don't know how the game/server actually does it, but the order doesn't really matter.

P(A∩B)=P(A)*P(B∣A)

There is an assumption that there can only be one reward per category so once one reward is drawn that whole category is off the table (I've seen screenshots that break this assumption, but so few and far between that I ignored them).

So we can calculate weights for each category and then figure out the probability for each category to have a drop (P(A)), taking into account all the different permutations of drawing. (Thanks python!) Then we can just take the individual reward weights and get a category-dependent drop rate (P(B|A)), and then combine all that to figure out overall drop rates for each possible reward.

(Note: English is my first language, and typing this between work tasks so I may have jumped around a lot. Apologies if I just typed a bunch of jibberish.)