Error:
This Flatpak does not have write access to ~/.local/share/applications and ~/.local/share/icons, so it cannot install or uninstall PWAs.
Once you grant access to those two directories (Flatseal is the easiest method), you can attempt to re-create the shortcuts from chrome://apps.
Close.
Solution:
flatpak override --user --filesystem=~/.local/share/applications --filesystem=~/.local/share/icons com.google.Chrome # or your preferred browser