Where does firefox get the system theme from?

I am writing a bash script to switch system theme between dark and light whenever necessary (on Linux Mint 20.3). I could make it work for the overall OS theme, the terminal theme, and some gnome applications on flatpak.

With this, I expected that Mozilla Firefox will switch theme automatically, as its theme has been set to System theme. However, the Firefox theme does not change. It would be helpful if someone could point me in the right direction to implement this.

In short, I am looking for at least one of the following:

1. The manner in which Firefox determines the system theme on Linux Mint.
2. The commands to force Firefox to follow a particular theme.

Thanks in advance. Here is my bash script:

#!/bin/bash
if [ $# -eq 0 ]
then
    echo Current Theme: $(gsettings get org.cinnamon.theme name)
elif [ $1 == "dark" ]
then
    gsettings set org.gnome.desktop.interface gtk-theme 'Yaru-dark'
    flatpak override --user --env=GTK_THEME='Yaru-dark'
    gsettings set org.cinnamon.theme name 'Mint-Y-Dark'
    gsettings set org.cinnamon.desktop.interface gtk-theme "Mint-Y-Dark"
    gsettings set org.cinnamon.desktop.wm.preferences theme "Mint-Y-Dark"
    gsettings set org.cinnamon.desktop.interface icon-theme 'Mint-Y-Dark'
    gsettings set org.gnome.Terminal.ProfilesList default f02cd96e-20b4-4146-a6aa-75f5da6a65b2 
elif [ "$1" = "light" ]
then
    gsettings set org.gnome.desktop.interface gtk-theme 'Yaru-light'
    flatpak override --user --env=GTK_THEME='Yaru-light'
    gsettings set org.cinnamon.theme name 'Mint-Y'
    gsettings set org.cinnamon.desktop.interface gtk-theme "Mint-Y"
    gsettings set org.cinnamon.desktop.wm.preferences theme "Mint-Y"
    gsettings set org.cinnamon.desktop.interface icon-theme 'Mint-Y'
    gsettings set org.gnome.Terminal.ProfilesList default b1dcc9dd-5262-4d8d-a863-c897e6d979b9
else
    echo "Unknown argument"
fi