Most DEs do include the file manager in the default applications menu. You can also use xdg-mime to set it as the default for inode/directory
Until some app doesn’t care about xdg-mime. At least I had some issues with firefox a while ago.
Firefox uses xdg-mime or xdg portals, depending on the configuration of the package. If you are using it as a flatpak, it will use portals.
Apps using portals will use the file picker your portal provides. This will usually be either the GNOME or Plasma file picker. Note that this file picker is separate from your default file manager.
It wasn’t about the file picker but the file manager that opens after clicking the button to open the folder a downloaded file is saved in. It was indeed flatpak firefox iirc.
It did work at some point but broke again… At the moment it works I believe (at least I didn’t get a call from my mom about the file manager being wrong again).
