Thanks, RED, for summoning help!
Thanks, Schlitz, for the directional advice.
It took me a bit to figure out how to get the trim all off, but when I got there I believe I found this:
https://www.grohe.us/Rough-Valve-Spa...HROME-47860000. Which I could figure out how to remove, but not how to disassemble to try to find any interior filters.
There was some crud on the circular filters, and I cleaned that.
(I think) more importantly, the left hand water line that connected into this thing had just some random plastic hanging loose (kind of like a shred of a thick plastic bag)? It felt clearly not supposed to be there, so I got rid of it, put the thing back together enough to test it, was impressed by the results, and put everything back in place (after a nice cleaning).
If I were more confident I would try to turn off the water further upstream, open the water line that had the plastic stuck in it, and make sure there isn't more up there. I'd only turned off the line with the screw immediately next to the pressure control, so couldn't open the line without spraying water all over the place. At least next time I'll know where to look, and now I have the confidence that if I need to replace this pressure thing I know it's a 10 minute job.
Thanks! I'm excited to take my first non-depressing shower in months.