As of now, the flatpak Gtk4 apps only support Adwaita, Adwaita-Dark and Yaru-* (if installed) themes, but there is a workaround.
You can set all GTK-4 apps to use it. To do that, you need to set the theme for non-flatpak GTK3 and GTK4 apps and for flatpak apps using GTK3 and GTK4.
Non-flatpak GTK-3 apps
Use gnome-tweaks. Change it in the appearance section.
Non-flatpak GTK-4 apps
Set an option in your theme's installer to use libAdawita. The theme that I use (Orchis) has this option. If it doesn't, or does not have an installer, copy the files in ~/.themes/[Your-Theme]/gtk-4/ or /usr/share/themes/[Your-Theme]/gtk-4.0/ (where Your-Theme is the name of your theme) to ~/.config/gtk-4.0/. You'll have to override the default Adawita stuff there, so back it up if you're concerned.
Flatpak GTK-3 apps
Install your theme from Flathub:
flatpak install org.gtk.Gtk3theme.Yaru-dark
(in this example, we use Yaru-dark)
If your theme is not not on Flathub (it likely isn't), you can use these commands to allow them to read the folders, and use your theme.
sudo flatpak override --filesystem=$HOME/.themes/
sudo flatpak override --filesystem=$HOME/.icons/
(the latter command will also allow them to use your icon and cursor packs)
Flatpak GTK-4 apps
Give apps permissions to access it and set the GTK_THEME environment variable for them. I used flatseal, but it can be done via flatpak cli.
The /usr/share/themes/ folder is blacklisted in Flatpak, so that can't be set. I've tried symlinks, but they don't work. You have to copy (or move) the theme to ~/.themes/ or another folder you store your themes in.
sudo flatpak override --filesystem=$HOME/.themes/
sudo flatpak override --env GTK_THEME=Yaru-Dark