Just from watching how people react to it at the table I play at, yah know what's terrifying and poison-appropriate? Damage over time. Take 1 damage at the beginning of each turn. Take 1d6 at the beginning of each turn. Take 2d10 at the beginning of each turn. Now it actually feels like poison, and the player is spooked because 1) they're taking damage every turn, and 2) that interacts in particularly unfavorable ways with death saves.
And yes, rider effects. That is exactly what poison should be able. Failed your save, and now you have disadvantage on ability checks and move at half speed. And take 1d6 damage at the beginning of every turn.
If DND wasn't DnD, I'd be more in favor of this. But for these kind of "death spiral" rules to be used, the game has to be WAY more deadly than DND is generally known for, and also have a way different attitude towards combat. DND is heroic rock em sock em robots. Characters can throw themselves into battle and beat the odds because they're that good. If barbs and fighters get worse at doing their job as they're doing their job, the game entirely changes. Characters don't fight melee, if they can avoid it. They carefully plan unfair encounters, and use bows (ideally) and pikes (if they have to). Not saying that's bad, it's just not DND.