I have a little bit of follow up on my issue, for those of you who may be interested:
TL;DR:
- iOS 13.3 was not to blame (at least, not directly)
- Older iPhones may benefit from the occasional clean out
- Do not fill your phone's drive to absolute capacity without expecting consequences
The rest:
I took my wife's 6S which was draining battery like no one's business after the update to the Apple store for some diagnostics. The short of it is that the update doesn't seem to have been the cause. I suppose it may have done some kind of system juggling that then somehow buggered things up, but the OS itself seems to be fine.
When a diagnostic was run, the hardware came out clean, so the technician helpfully looked into the software and it seems the phone had a couple of issues that "made no sense". One was that the multitasking 'card view' was creating two separate stacks behind the scenes which were eating up resources as the system tried to maintain them. These additional stacks should not have been created at all, never mind maintained, and so that was a pretty big suck of resources. The memory was also doing some kind of refresh behind the scenes at intervals that it shouldn't have been doing. Apparently according to the logs this problem has been happening for over a year with this device, and doing that will slow it and consume more resources for essentially no reason that the technician could see (as stated, the hardware came out clean). So these issues were probably specific to this particular iPhone.
Finally, there were two rather large system files just kind of hanging out on the phone. These could be seen at the very bottom of the iPhone storage screen in settings, one titled "System" and the other titled "Other". According to the technician there was some kind of disconnect between the size of these files and what their function is. Together they totaled nearly 10GB of phone storage, which apparently is excessive.
All of these issues, I was told, would be solved by restoring the iPhone using iTunes. I was assured that if I did an encrypted backup and restored from that backup after restoring the original OS software, that all would be well. So, I went home and hooked up the iPhone to the Mac for the first time since late 2018.
Having completed the process (took a while), with only a few hours of actual use, I can say that the phone is indeed much happier, and the battery drain issue appears to have resolved, although I won't be able to say for sure until I get a report on how the day went. Still, the first couple hours seemed quite reasonable, with the phone losing only 3% power in the first couple hours of today.
The consequence of this was that in spite of being assured that everything would return to exactly where it was, my wife still needed to re-designate her fingerprints for the sensor, and she noted that the phone seems to have forgotten everything it learned about her typing patterns (i.e. the suggested words banner when entering text no longer predicted the same words it has for years). Otherwise, all seems pretty decent.
A little postscript here is that after I got through with my wife's phone, I checked my own iPhone 11 for the huge system files. They exist on my phone too. "System" and "Other" are both around 6Gig, so that made me wonder what exactly these files are doing there. An internet search provided the following possible answer.
That significant Other or System Data filling up all your iPhone storage? Here's what you can do about it.
www.macworld.com
In the case of my wife's phone, her storage was creeping up close to the limit of the device (photos+kids=storage disaster), so having less space on the SSD to work with also made for the phone having to work harder and less space to do things which I assume impacts performance and battery life. So, for those of you with similar issues, clearing this out might be helpful.