As mentioned in the postings before I ordered a replacement for my AWU at Amazon, which arrived last week (took longer as expected ...).
The first watch had the dim issue, so I could hardly or not at all read the display in darker surroundings.
Now, the second watch (SW ver 9.1) shows the same behaviour with display "always on" option turned off, BUT by switching the display to "always on", the screen brightness of all apps, selection screens and in "always on" mode in darker surroundings is much better compared to the first UWA and really acceptable, even it is not the level of a series 4 watch.
The first UWA did not show any difference, it was too dark with "always on" option turned on or off.
This is really strange and indicates, that the issue may not or not only be a software problem.
It may be the case, that there are different brightness sensors built-in the watches, so a software update may have different effects.
I would assume, that this is the case, because my first watch showed a different behaviour after updating it from beta 9.02 to 9.1. And this was strange as well. With 9.02 the screen was too dark in general as long as I was in a darker surrounding. After the update the app selection screen was brighter than before, but by starting an app it got really dark again, so the display was not readable. Switching back to the app selection screen, the display was brighter again.
I checked this behaviour many times, the effect was reproducible.
There are many postings in different Apple watch forums in this matter, starting with series 5, but I am not aware of any related statement by Apple. The Apple support specialist I talked to told me, that this issue is not known at all.
Anyway, I hope, that it will be clarified soon.