Update & Interim Summary - No Solution:
My opening question(s)¹⁾ and the newly upcoming one²⁾ have not be answered.
¹) @Zauberer-Merlin’s suggesting ‘savedesktop’ is closest to the overall target.
It reduces the effort of what I’d done manually by >90%, but … it achieves nothing beyond.
(The original question was about “How can Gnome be convinced to respect its settings?” …
… and it still doesn’t, no matter whether the named two (of several hundred) settings (‘attach modal-dialogs’ and ‘accent-color’) have been set manually or imported by savedesktop.)
²) The state of “23ed538” (the older “desktop computer”) is now more up-to-date than that of “25hc780” (the newer “laptop”) …
… which I - again - installed from scratch with the ‘manjaro-gnome-25.0.3-250526-linux612.iso’ but let it ignore all of the ~300 updates of June 28. I’ve set up Timeshift and taken snapshots after each installation of additional Apps and after importing “23ed538”'s savedesktop. And it still shows the basically working GUI.
From the start of my trials to set up the laptop after taking the first hurdle with installing Manjaro-Gnome, 7 weeks (!) ago, I’ve been trying to find the difference of the two systems which is responsible for the different behavior, with ‘accent-color’ catching my eye as the first one.
This has lead to some false guesses and the slightly misleading title of this topic. (It’s not about differences of Gnome 48.0 and 48.1 - both machines now run Gnome 48.2. - And the broken display of the laptop system after the update of June 28 is OT regarding that title.)
Maybe time to spawn two (or more) topics from this one. And I’m thinking about doing that in the German sub-forum to lower the hurdle to post here (since my confidence in my command of English has been sort of shattered by misunderstandings that have started those 7 weeks ago and since then make me need another and yet another attempt before I hit the ‘Reply’-button).
p.s. edit:
I’ve now indeed been able to correct the topic title, what hasn’t been possible after >2 weeks after its start.
Perhaps an effect of the new “member” status?