At what level of battery health does iOS begin to throttle performance? I have an iPhone SE running iOS 10.3.3, planning to upgrade to iOS 13. A third-party app indicated I can charge to about 80% of my battery's capacity. I know that right now it lasts less time than when it was new, but it still works pretty well and is perfectly fast. I also know that iOS 13 drains battery faster than iOS 10. But at this level of battery health, would iOS 13 be an additional problem that results in performance throttling which wouldn't happen in iOS 10?
When you go to Settings -> Battery -> Battery health you see the capacity of the battery. That number indicates the power storage capacity of the battery relative to a brand new battery. It does not directly indicate the health of the battery in terms of what you are asking for, therefore the question cannot be precisely answered in the way you have asked it.

You want to know when power throttling starts, but that starts after the iPhone has noticed that there has been an unexpected shutdown due to the battery not being able to deliver enough power during a peak power consuming operation. That is therefore not the same as the battery's capacity, but has to do with how much power (or amps if you will) that battery can deliver in bursts.

There is definitely usually a correlation between the capacity and its peak power delivery capability, but there is no direct relationship. Power storage capacity is one thing, peak power delivery capability is another. 

iOS can only report directly and a priori on the first. The second is a matter of learning 'the hard way' that the iPhone asked for too much power during some operation, therefore experienced an unexpected shutdown, therefore iOS will thereafter, unless you disable it again in the same Battery health screen, run in throttled mode, so as to not have the same thing happen again.