Today I replaced the brake pads and the old ones on the creaky side were worn more at one end, so presumably there was less pressure at other and the creaking was from the brake trying to twist things.
The caliper seemed to slide but after pulling it off the pins and cleaning and greasing things it slid a little more easily. The two pistons were spotless after 10 seconds with soapy water and they came out evenly when I applied pressure on the lever, so nothing seized there.
The retaining pin for the pads, the pressure plate they bear on at the other end, and the anti chatter spring, were all very dirty and corroded (as they always are). To explain the asymmetric pad wear it would need something like the pad not sliding on the pressure plate. I cleaned and polished those items and applied a thin smear of copper-slip.
I did both sides the same and there’s no creaking so hopefully it’s now sorted. Test ride tomorrow…