Okay, late update and developments. First of all, I had forgotten this thread.

And I evidently forgot to mention that the issue was a bad LR sensor, which, when replaced, made the whole system come back online. Until c. a couple of weeks ago. What I didn't see this time is that alarming screen in the OP pic. For most of two weeks I've been seeing the stock (startup) screen that says, "Tire Pressure: Drive to Display", and no tire warning icon in the dash.
Today was my appointment to go into Wheel Werks and find out what is what. They found the RR sensor dead.
What should have been a simple TPMS sensor replacement turned into an all afternoon back and forth journey, seeking the answer to why the TPMS screen won’t display. I left Wheel Werks before eleven-thirty and kept waiting for my psi readout to come online: clear down to 104th South and Bungler, where I gassed and shopped a few items at Costco, then home, where I called Wheel Werks and said I was coming back in.
When they scanned all four wheels, they found that the RR sensor had “unprogrammed” itself: Ray reprogrammed it, I went around the block and the psi screen came back to life (as I came around the last corner). Kelly evened up the psi in all four tires to 43 psi and I was on my way. But as I was about to exit I-215 at Redwood Rd, the psi numbers suddenly were replaced by that startup screen, so, back to Wheel Werks I went.
Ray went around all four wheels and the TPMS sensors all indicated good to go. All he could say was, “Go drive around some more and if that doesn’t work, I’ll put a new sensor in”.
I went down to Jerry Seiner and James was very helpful: he got one of the techs to hook up the diagnostic reader: it showed all four sensors good, but no psi readouts: he went out for c. twenty minutes in my car and reset everything, but the reset didn’t take. He said that he was reading an error (I can't recall what he called it). “I’ve never seen one go bad before, but I’m thinking it must be the TPMS sending module” (near as I can recollect what he called it).
James said that Kia would refuse more diagnostic work to ID the issue unless the OEM TPMS sensors were on the car, so, I needed to change wheels and see if (first of all) that made a difference, which, if it did, would show that the issue was caused by the aftermarket sensors on my TSW wheels. Also, the tech said to try lowering the psi to 38 and see if that was more “acceptable” to the TPMS sending module/system (that sounded pretty far-fetched, but hey, if I was told to try it, I’d try it).
Back to Wheel Werks I went and explained the situation, vis-à-vis needing to try the lowered psi on my way home, and later, swapping to my OEM wheels and sensors when that didn’t work. Kelly lowered the front tires to 38 psi and the rear tires to 36 psi: and the drive home changed nothing, the TPMS system remains comatose.
I'll get around to swapping my summer wheels to the OEM wheels and sensors. That won't change anything (bring anything TPMS related back to life), or I will be very surprised: after over three years of flawless operation on two sets of wheels, why would putting OEM back on change anything? It has to be the TPMS "sending module" (or whatever they call it).