So on my server, I want to make it so that even OPs can be kicked or denied login due to being drunk. I have tried this by negating the permissions for EVERYONE, including for OPs.

This is how I have made it in the permissions.yml file in the server directory.
server.brewery:
description: Brewery overdrink permissions
default: false
children:
brewery.bypass.logindeny: false
brewery.bypass.overdrink: false

However, no matter how I try to take away these permissions from the OPs, they are ALWAYS able to bypass overdrink or logindeny.

Tried it with LuckPerms and setting the permissions to false works perfectly fine

Maybe you should reduce the OP level in server.properties. Or simply remove OP and use only permissions (longer but easier for the future).