Currently while using the /brewery drink command, it messages the player "[Brewery] You drank one ". Is there any way to disable that? I don't see it in the config.

No there is currently no way to disable this. Why do you need to disable the message? An Alternative you could use would be the /brew <Player> <alc> command, where you can set the alcohol level of a player if that is suitable to you

I considered using the /brew command but it didn't seem to have a way to increase the player's drunkenness based on how drunk they already were: It wouldn't increase their drunkenness incrementally.