Install Flatseal which is a graphical utility to review and modify permissions from your Flatpak applications (use console if you’re comfortable).
Set these parameters
XDG_SESSION_TYPE=wayland
OBSIDIAN_USE_WAYLAND=1
The Flatpak install of Obsidian will now work correctly.
Alternatively update your Flatpak Obsidian installation which includes now these parameters as standard.
I found the maintainers of the Flatpak version of Obsidian to be very responsive.