Chrome doesn't detect light/dark theme change on Linux (KDE/Flatpak)

### Bug Description
Chrome does not detect light/dark theme change in the system.

### Steps To Reproduce
- Install Chrome via Flatpak (Flathub repository)
- Launch Chrome
- Switch Gnome to light/dark mode:
```
dconf write /org/gnome/desktop/interface/color-scheme "'prefer-dark'"
# or
dconf write /org/gnome/desktop/interface/color-scheme "'prefer-light'"
```

### Expected Behavior
Chrome should follow system theme change.

### Actual Behavior
Chrome theme doesn't change.

### System Information
```
$ lsb_release -a
LSB Version: n/a
Distributor ID: SteamOS
Description: SteamOS Holo
Release: rolling
Codename: Holo

$ uname -a
Linux steamdeck 6.1.52-valve16-1-neptune-61 #1 SMP PREEMPT_DYNAMIC Tue, 06 Feb 2024 00:51:49 +0000 x86_64 GNU/Linux

$ flatpak info -m com.google.Chrome
[Application]
name=com.google.Chrome
runtime=org.freedesktop.Platform/x86_64/22.08
sdk=org.freedesktop.Sdk/x86_64/22.08
base=app/org.chromium.Chromium.BaseApp/x86_64/22.08
tags=proprietary;
command=chrome
required-flatpak=1.8.2

[Context]
shared=network;ipc;
sockets=x11;wayland;pulseaudio;pcsc;cups;
devices=all;
filesystems=host-etc;~/.config/kioslaverc;xdg-music;xdg-pictures;xdg-videos;/run/.heim_org.h5l.kcm-socket;~/.config/dconf:ro;xdg-download;xdg-run/dconf;xdg-documents;xdg-run/pipewire-0;

[Session Bus Policy]
org.freedesktop.Notifications=talk
org.freedesktop.FileManager1=talk
org.mpris.MediaPlayer2.chromium.*=own
org.kde.StatusNotifierWatcher=talk
org.freedesktop.ScreenSaver=talk
org.freedesktop.secrets=talk
ca.desrt.dconf=talk
org.gnome.SessionManager=talk

[System Bus Policy]
org.freedesktop.Avahi=talk
org.freedesktop.UPower=talk
org.bluez=talk

[Environment]
GSETTINGS_BACKEND=dconf
GIO_EXTRA_MODULES=/app/lib/gio/modules
GTK_PATH=/app/lib/gtkmodules
DCONF_USER_CONFIG_DIR=.config/dconf

[Extra Data]
name=chrome.deb
checksum=50380ed6c27b6e08054deec2dfa0a71d85e31bdaccf99a8508eccdc880e94346
size=106428268
uri=https://dl.google.com/linux/chrome/deb/pool/main/g/google-chrome-stable/google-chrome-stable_121.0.6167.184-1_amd64.deb

[Extension com.google.Chrome.Debug]
directory=lib/debug
autodelete=true
no-autodownload=true

[Build]
built-extensions=com.google.Chrome.Debug;com.google.Chrome.Sources;
```

When natively installed from AUR, Chrome doesn't have this problem.

Reproduce the issue with the Flathub installation using the provided dconf commands, then compare its Flatpak metadata and environment from `flatpak info` with the native AUR installation. Investigate the theme-change integration and consider the issue done when Chrome follows subsequent light/dark system changes in the Flatpak build.

Written by the indexing model from the issue text.