Just a bit of background or possibly helpful info on pulse vs continuous discharge ratings. In RC (radio controlled) models, lipo batteries are used which is short for lithium polymer. As far as I understand they are a lithium-ion battery. They usually come with a labelled continuous discharge and a "pulse" or short term high discharge rate. For example, it might be labelled 1000mAh, 25-50C, meaning 1000mAh capacity, 25C continuous discharge and 50C for short bursts. C is the mA of the mAh rating, so 25C = 25 x 1000mA = 25A. If you abuse the ratings, as a modeller, expect shorter battery life at the least, and destroyed batteries at worst. In regards to PV's, I don't think vaping would be considered continuous discharge, moreso burst or pulse discharge, that is just my observation and not to be considered to have any authority.
To sum it up, continuous and pulse ratings for Lithium batteries are nothing new to RC modellers who have been using them for quite a while. Perhaps it would be safer for vapers if manufacturers gave both continuous and pulse ratings if the battery was intended for vaping. Another step forward perhaps.
Here is an example of lipo labelling in this pic. BTW RC (radio control) modellers are as fanatic about their batteries as vapers, if not moreso. If a given battery "does not deliver the goods" everyone will know about it soon enough. This mod has two 750mAh batteries in parallel, for a total of 1500mAh capacity. 35C continuous and 70C max for a short burst. The atty is 14mm diameter to give a size reference.
Keep in mind that there is no free lunch with lithium batteries in general. If a manufacturer claims a higher pulse or constant discharge current (for the same mAh capacity) then there is going to be a trade-off in weight or size or life cycles or cost, or they have come up with an improved chemistry or battery structure.
Maybe its time that batteries sold specifically for vaping are supplied with a continuous discharge and a pulse rating.