Perhaps HP damage in such a system isn't the best way to model such a condition? Tasha's sounds more like AC, Attack, and Dex-check penalties to me.
Although in this case, I would argue that you could sustain a heart-attack, stroke, head injury, or seizure. I mean, it is magical laughter, innit?
Nonetheless, strictly non-damaging conditions can be handled in multiple ways in a hp=fatigue system including more traditional modifiers to movement, etc. and supplanting the standard wound conditions when 0hp kicks in. The only conditions that really matter in such a system are the SoD conditions. So for example, Hold Person might deal <X> damage and impose a movement penalty. If you are reduced to 0hp while still held, you freeze in place (or whatever) instead of rolling on the wound table. In the harder direction, being reduced to 0hp while engaging a Medusa means you've looked at her and are turned to stone. Whether that means she has some additional damage/round effect to represent the difficulty of fighting without looking is optional.
Just because 0 HP would represent any condition that takes you out of the fight doesn't mean that all conditions have to be represented that way.
I think it's fine that some attacks that reduce a character to zero hp aren't fatal. The "damage" can be remedied by a number of means. If you are petrified you need a
flesh to stone spell, if you are laughing uncontrollably you need a short rest, if you sustain a slashing attack you need a band-aid and time to heal. Sometimes the remedy is suggested by itself but this can be catalogued too.
I'm no fan of conditions that alter a character's stats because it slows down the game and is sometimes conveniently forgotten about anyway. I'd rather see fewer hit points across the board. As I see it you either have hp or you suffer the attack.
The medusa is an interesting example. I agree it petrifies a character at zero hp. Avoiding the medusas gaze is no different than avoiding a marauder's axe. It should be part of the medusa's stats to begin with. I mean this game of ours features anything from rotgrub to dragons, it is a tall order to make simulationist rules for all of them.
Consider this: You are down to single digit hit points. I attack you with a disarm attack that sends you down to zero hp; your sword flies away. Now you have zero hp and no sword. Why won't you simply give up or runaway? By now I know I can do anything to you. I can chop off your head - or belt making you drop your pants. Maybe non-combatants have zero hp all the time?
Just think of the RP opportunities. Different classes would have access to different damage tags. Wizards would have sleep and fire attacks, rogues would have knock outs and non-lethal tags, fighters would have slashing, piercing, bludgeoning, disarming and pinning attacks.
Here is another example for you (thanks for reading): A dire wolf attacks a ranger carrying an axe and an empty hand. The ranger can make attacks that does 1d8 slashing or 1d3 grappling. If the ranger does grappling attacks the wolf is considered free from lock or hold until it drops below zero hp. The tactic for the ranger might be to wear the wolf out with the axe first and then grapple the animal to the ground as the wolf grows weaker.
Why bother having rules for grappling when we've managed to live without rules for clinch for forty years?