Instead of directly giving you special effects, I think it'd be better for drinks to boost your attribute gains. A QoL update for attributes is scheduled to happen at some point, and I think giving certain drinks the ability to boost your attributes would be helpful for those who haven't maxed everything out yet.
To provide an example, say drinking Beast will give you a 10% buff to your speed for 10 minutes. It's not too terribly realistic, but neither is slamming your head against a short ceiling 1,000,000 times for like 2 full OOC days or running around with a melon launcher (which totally isn't cosmetic abuse) until you're running twice as fast as a normal minecraft player.
Clearly, if we were to implement something like this, we'd need to take measures in order to make the drinks fair and balanced. Perhaps, performance boosting drinks could be set on a cooldown timer? Maybe they could only be available in certain vending machines / shops? Maybe after the buff expires, you'll suffer from a debuff which makes you slow or "tired?" Perhaps, there could even be a form of steroid sold on the black market, which would give you better gains at a higher price and risk.