You're right, it does look pretty bad.
This appears to be some quirk when using the elementary icon theme with Geary.
It's possible to set the GTK_THEME to the Adwaita icon theme which looks much better.
You can set the theme when running Geary with the following Flatpak command.
flatpak run --env=GTK_THEME=Adwaita org.gnome.Geary
To avoid the hassle of ...
The problem of the 'unmet dependencies' on elementaryOS 6.0 appears to be solved when installing the elementaryOS 6.0 public beta from their April 30 build (I was still on an apt-updated install of the April 28 build before).
So it appears that we can use the 6.0 public beta to work on elementaryOS apps at the moment.