To elaborate on the behavior, it isn't that it begins recording a couple seconds after hitting the record button, but rather the recording begins immediately and the record level ramps up in volume from very low to the normal recording level over a period of actually more like five seconds. You can actually faintly hear the tail end of the "now recording" ding at the beginning of the recording (which I've also never noticed before). Essentially the ramp up acts like a fade-in. (It's almost like the "Reduce Loud Audio" headphone volume protection feature operating in reverse.)
Also, importantly, the ramp up in record level doesn't begin happening until sound is being produced for the mic to record. You can't just hit record, wait a couple seconds, and then start speaking, playing an instrument, or whatever and it will be at the normal recording level. Yes, I suppose a workaround would be to hit record and speak "testing one, two, three" and repeat that three or four times, until you're at the normal record level, and later trim that bit out of the final edit. But come on, that's an unrealistic fix and outside the convenience we otherwise love about the device.
This iPhone has never been jailbroken. Nor have I ever backed up any iPhone prior to an iOS update—never even heard of that before (although I should probably consider it going forward). And I'm not necessarily attributing the change in Voice Memo behavior to, or blaming it on, the recent iOS update, but merely noting the coincidence—Voice Memos worked correctly prior to the overnight automatic update and the next day this problem appeared. There are no other apps open that are using the built-in mic, nor any external mics connected to the phone (by cable or bluetooth).
It really seems like some other sound or mic related app setting got toggled in the update, but I've tried everything I can think of and just haven't landed on it yet.
Thank you!