Thanks for the replies, gents.
As a further test / clarification, I went ahead an applied a threshold adjustment (in Affinity Photo 1.6.4, Layer -> New Adjustment Layer -> Threshold Adjustment) to the original versions (i.e., 16-bit TIFFs, not JPEGs) of the two files I posted above--to make any changes easy to see. First I tried a threshold of 95%, and still saw all white--no differences of 5% or more, at least that I noticed. Then I tried a threshold of 99%, i.e., a difference of 1%, and found a slight peppering of black dots, indicating pixels where the JPEG differed from the TIFF by 1% or more, but less than 5%. Finally I tried a threshold of 99.6%,* which is right at the limit of what you can represent with 8 bits**--and a lot of pixels were black, indicating some difference. All three graphic outputs are attached, in order. These results are far easier to digest than are trying to visually assess shades of off-white, which is what my prior post gave you. Hopefully you'll find the new versions useful.
What do they show? Well, are you a 'glass half empty' or a 'glass half full' sort of person? As far as I noticed, no pixel showed a difference of 5% or more between the ProPhoto RGB JPEG and the ProPhoto RGB 16-bit TIFF. The fraction of pixels that showed a 1% difference appears to be very small (probably not 1 in 1000 pixels, and certainly not 1 in 100 pixels), and very scattered around. not contiguous. On the other hand, the fraction of pixels showing a difference that 8-bit graphics can represent was not trivial--far fewer than half, but my visual guestimate says maybe 5% or 10%.
So even if you print on a printer / through a printer driver that is limited to 8-bit precision, it appears that it would be inaccurate to say that there is no difference between a ProPhoto RGB JPEG and a ProPhoto RGB 16-bit TIFF. On the other hand, I feel quite comfortable saying that the differences are so small that 95+% of us could not reliably detect them in 95+% of photographic images.
* Affinity Photo only displays thresholds in even percents, e.g., 99% or 100%. However, the on-screen appearance shows quite clearly that it is performing the appropriate, and different, operations depending on whether you set the threshold to, e.g., 99.6% or 99.9%.
** I realize that an '8 bit' color image uses 8 bits for each of the red, green, and blue channels. So there are 256 possible values (0 to 255) per channel. I'm assuming that a change of 1 out of 256 or 0.4% in any of the three channels would be 'picked up' by the 99.6% threshold, but I don't know exactly what Affinity Photo is doing, math-wise.