[Q] Poisoned Weapons: Multiple Rounds, Multiple Targets?

I remember this being asked before, but I don't think there was a definitive answer (and now I can't find the thread), so I'm asking this again...

I have two questions relating to poisoned weapons:

(1) Does the poison on a weapon get used up on the first hit, or will it work multiple times?

The rules say: "The poison takes effect the next time the weapon hits and deals damage." - Does the use of the word "next" mean ONLY the next time, or does it mean "next and subsequent"?

(2) If the answer to the first question is "it works multiple times", then will the poison work against multiple targets if you hit each target on a different round?

The rules say: "If a poisoned weapon hits multiple targets, the poison attacks only the first target hit." - Does this refer to hitting multiple targets in the same round, or hitting multiple targets in the entire encounter?

Thanks!

I read the rules as "only on the first hit"
that the second part makes more sense with this ruling solidifies my opinion.

Yes, that's the conclusion I came too.

DMG 51, Poisoned Weapon Attacks: ... If a poisoned weapon hits multiple targets, the poison attacks only the first target hit.