How fast is "Recover X% Life"?

are effects like the Hired Killer notable passive ("Recover 2% of life on kill") instant? Or do they happen over some period of time?

One would assume they are instant, since there is no mention of this happening over any period of time

But the Patient Reaper trickster ascendancy conditionally increases life, mana, and ES recovery rate by 70%, in addition to also granting percentage recovery on kill. Again, it mentions no span of time over which that recovery occurs. The PoE wiki tells me that increased recovery rate does not apply to instant recovery like Lifegain on Hit since there is no "rate" to affect.

So does that mean Patient Reaper does not increase its own recovery? Or is this just another bit of obtuse writing where there is a period of time over which it is recovered, but that period of time is simply not mentioned anywhere?

Recover x% is instant, patient reaper increases any form of recovery over time.

What is "instant" does not have any rate. so there is nothing to be increased

hmm
so even if you have killed someone recently with your DoT, patient reaper will still only recover 3.0% and not 5.1%?

well, it removes some of the synergy I'd assumed the skill had, but at least it's consistent wording.

A somewhat related question: does Weave the Arcane's chance for mana recovery apply to triggered skills like counterattacks and cast-on-X supports?

Nah, triggering is not using by you.

"using a skill" requires pressing a button to do so