To answer the unspoken question, yes; I suck at naming things. You are now stuck with "MapVote-Bot". No, this is not just for Overwatch Tournaments. You should be able to change the sets to anything. I made this as readable as possible so you can adapt it to your use cases. Permissions needed: Bot - Send Messages & Read Message History If you get "interaction failed" you likely didn't give the bot permissions to send and view messages in the channel you're using it in.
The screenshots below are no longer up to date - Assault Mode and the Samoa map have since been added. The minimum amount of modes to choose is now 4 rather than 3.
The overlapping category is picked. If there are multiple overlapping it is picked from them at random.
If at any time the other captain tries to select something when it's not their turn, this is what they'll see:
Final Result: