I'd like to give an update on my situation. To sum up: the eyestrain is still there, but overall it's better than before.
I have spent the last three months with the following settings:
Color profile — HD 709-A (please see this thread: https://ledstrain.org/d/768-colorsync-on-macos-what-is-this-could-it-be-a-culprit )
Resolution — default for display: 2560x1440 HiDPI
Color depth — Millions of colors (with SwitchResX), 24 bit in About this Mac
Automatically adjust brightness — OFF
Brightness — at about 55%, but never below 50%
Night shift — OFF
Font smoothing — OFF (with TinkerTool)
All possible animations — OFF (with TinkerTool)
Windows under Parallels — only integer scaling, currently at 300%, Best for external displays, Coherence
Occasionally, when my eyes get tired, I launch Gamma Control, and it gives me a small relief. I think it's because different muscles get strained with it. I cannot use this program all the time, because somehow iMac screen "required" high brightness.
When I turn on the Mac in the morning, I can work for some time without feeling strained, but at some point the eyes feel very tired, as if they were doing extraordinary work. How long I can bear, depends also largely on my physical condition, as well as on the program I use. E.g., Safari is the easiest on the eyes.
I immediately feel relieved when I boot into safe mode. The screen feels stable, and I can relax looking at it, as well as think better, without something straining me all the time.
There should be dithering involved, no doubt.
I have examined other Macs in the store, spending quite some time with them. The 13-inch MacBook with Intel graphics feels the best of all (SeniorTaquito, thanks for the tip), but I'm hesitant as I do not know how it will behave in the long run. I'm also not a big fan of laptops.
Basically, all the Macs look good in the store owing to super bright ambient lighting and the fact they are always displayed at 100% brightness themselves. E.g., iMac Pro looks just fine. But I have to say that the new 16-inch MacBook has the worst screen of all: I start feeling dizzy simply looking at it. I assume that some really bad technology has been used to make this cheap display look better.
Can other Mac owners please share if they also feel better in Safe Boot (boot with Shift pressed)?
If you have time, can you also try the above color profile? I had most relief of all my tweaks when I switched to it.