Comment # 4 on bug 1227479 from Jimis Hol

(In reply to Alynx Zhou from comment #3)
> 
> Did you have xdg-desktop-portal-gtk installed? It should get system wide
> dark mode setting via portal. Try install that. And maybe you should also do
> this: https://github.com/i3/i3/discussions/5896#discussioncomment-8556941

Yes it is installed. The xdg-desktop-portal and xdg-desktop-portal-gtk are the
only relevant installed packages.
What was missing is the $HOME/.config/xdg-desktop-portal/ directory. I created
along with file $HOME/.config/xdg-desktop-portal/portals.conf where I put

[preferred]
default=gtk

After reboot, the problem is solved. gnome-clocks and its timers work in dark
mode.
Thank you, thank you, very much.

P.S.
I was so excited that I added gnome by

default=gtk;gnome

and installed xdg-desktop-portal-gnome, that i excluded it due to bug
id=1210065 as i mentioned. Unfortunately, not only issue id=1210065 remains but
ruins dark theme too. So, excluding xdg-desktop-portal-gnome from installation
and creation of $HOME/.config/xdg-desktop-portal/portals.conf with default=gtk
IS JUST FINE.