I’m trying to understand better the boot and desktop environment loading sequence in order to understand where I can edit the $PATH available to the desktop environment before it loads.
I have Manjaro’s XFCE minimal distribution. I have installed Xmonad as a window manager.
In Manjaro’s login screen, I can choose XFCE or Xmonad. When picking one or the other, a basic $PATH is set somewhere, likely by whatever is launching the login menu program, and this $PATH is not influenced by .bashrc or .bash_profile.
What program is the GUI login screen? It doesn’t seem to depend on .xession or the like. How can I configure it?
I think you mean the Display Manager, which if you have not changed anything, should be LightDM for the XFCE edition. See more about it here: LightDM - ArchWiki
.bashrc and .bash_profile only affect the user’s bash, so the terminal.
The display manager for Xfce is lightdm, with the GTK+ greeter. You can configure it with lightdm-gtk-greeter-settings.
But that is likely irrelevant to your PATH issue.