The problem in a nutshell:
free drivers (both AMD and Intel): stutter when moving windows and in applications
Proprietary Nvidia driver: tearing

-> So the situation with any graphics driver is quite ugly.
I tested this with several GPUs, distributions and driver versions: The described problem is shared among all of them, and exists probably since the beginning of KWin 5.

I'm having a strong suspicion that the source of this evil lays in KWin's triple buffer detection.
What makes me think so? I tried several situations with the KWIN_TRIPLE_BUFFER environment variable and the results are very interesting.

First observation:
When KWIN_TRIPLE_BUFFER is set (both 1 and 0), the nasty initial "calibration stuttering" when compositing turns on disappears.
This easily noticeable when moving windows right after enabling compositing. KWin is the only compositor I know which shows such a weird behavior. It's especially nasty when you turned compositing off for a fullscreen application like a game, and when closing it and returning to desktop, everything is stuttery for some time.

Observation regarding Nvidia driver:
By default, there is tearing after the initial "calibration stuttering".
However, with workarounds, perfect KWin compositing is possible with Nvidia. To do so, set both
KWIN_TRIPLE_BUFFER=0
and in Nvidia xorg config, also
Option "TripleBuffer" "0"
The latter option makes triple buffering unavailable for any application and for some reason, it's required to make KWin compositing on Nvidia work correctly. It's completely free of stutter and shows low input latency at the same time.

Observation regarding free drivers (applies to both Intel and AMD to the same extent):
KWIN_TRIPLE_BUFFER=0 reduces stutter, but doesn't fully eliminate it in applications like Firefox. Weirdly, it also shows a much higher input latency than TB autodetect (environment variable unset) or than setting KWIN_TRIPLE_BUFFER=1.
However, KWIN_TRIPLE_BUFFER=1 shows stuttering when moving any window, e.g. Dolphin, and strong stuttering when e.g. scrolling in Firefox.
Unfortunately, there is no such an option in Mesa like Option "TripleBuffer", which is available in the Nvidia driver.
Instead, there is vblank_mode=x. But no value of it helps to reduce the stuttering or input latency of KWin. It's always stuttery and laggy.

I think it's very unsatisfying that kwin_x11 compositing does only work correctly on Nvidia with some workarounds and with free drivers not at all.
Shouldn't it be possible to bisect the issue due to the open nature of Mesa? It's quite the irony that, unlike any other compositor, KWin actually seems to hate free drivers more than the closed one of Nvidia.

The GUI options offered by KWin KCM in Plasma system settings don't have an effect on any of the points I described above.

It's still the same bug as 383023, but that original bugreport was too focused on Intel graphics. So I'm going to close it and I'm hoping for some response here.

I'm aware that kwin_x11 is left in "maintenance bugfix only" state, but the described problems can obviously considered as bugs and it would be a shame if kwin_x11 was left in that state.