it is not strange that these poisons don't use the term "poisoned condition" as most of the conditions don't use the added word "condition." For example, does not say "incapacitated condition creature."
This is different from the "Poison" damage type.
Poison condition only if the poison states that is an effect.
Now for the hard questions around poison.
How long does the poison last once on a weapon?
How many successful attacks can you make before needing to apply more poison?
How much poison in a day can you take from a poisonous snake animal companion, or imp familiar?
Why are they called poisonous snakes and not venomous snakes?
Serpent venom sells for 200gp a dose, how many doses can a druid milk from himself or have the party rogue milk from him in a day? Why do they adventure for gold when they could just set up poison shops?
See these are questions because no where in the DMG does it mention things like number of strikes or duration, we have to infer answers to these questions from monsters and npc's that use poison. The assassin for example seems to be able to strike multiple times per round, all combat long with poisoned blades.
Basic poison is of little help from the PHB, as it says.
Poison, Basic. You can use the poison in this vial to coat one slashing or piercing weapon or up to three pieces of ammunition. Applying the poison takes an action. A creature hit by the poisoned weapon or ammunition must make a DC 10 Constitution saving throw or take 1d4 poison damage. Once applied, the poison retains potency for 1 minute before drying.
"once applied, the poison retains potency for 1 minute before drying" - so basic poison lasts on a dagger for one minute after application but is it good for only 1 strike or all strikes during that minute. What about the other poisons mentioned in the DMG?
One last question, if the average assassin (the one listed in the npc section of the MM) can afford to use 1,200gp wyvern venom on both of his short swords, and all of his crossbow ammunition every fight just how much does he charge to kill people so he can make a profit? Where does he keep the pet wyvern?
I think the pricing is intentionally high because poison is not supposed to be an attractive option for most PCs (and that's potentally a lot of damage). I'd keep poison single-strike, but perhaps add a feat that lets it last longer for PCs who do want to specialize in it.I think I'm going to let poisons last for all weapon strikes for about a minute. The pricing is still just way too high. I'm considering having the listed prices apply to either 5 or 10 doses of poison (and assume that poison is usually sold in such increments).
I think the pricing is intentionally high because poison is not supposed to be an attractive option for most PCs (and that's potentally a lot of damage). I'd keep poison single-strike, but perhaps add a feat that lets it last longer for PCs who do want to specialize in it.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.