I've recorded this behavior here. The left monitor is HDR, the right monitor is standard. They are also different resolutions, which explains the size difference.
In this recording I have both the flatpak and the appimage installed.
The flatpak, when dragged between monitors, changes its color profile and permanently becomes oversaturated when viewed on the non-HDR monitor if at any point it is dragged to the HDR monitor, until next launch.
When the flatpak window is moved back to the non-HDR screen, the terminal outputs the following:
[2:0322/120305.102870:ERROR:ui/ozone/platform/wayland/host/wayland_wp_color_manager.cc:296] Unable to set image transfer function.
[2:0322/120305.102883:ERROR:ui/ozone/platform/wayland/host/wayland_wp_color_manager.cc:214] Failed to populate image description for color space {primaries:BT709, transfer:SRGB, matrix:RGB, range:FULL}
[2:0322/120305.103129:ERROR:ui/ozone/platform/wayland/host/wayland_wp_color_manager.cc:296] Unable to set image transfer function.
[2:0322/120305.103136:ERROR:ui/ozone/platform/wayland/host/wayland_wp_color_manager.cc:214] Failed to populate image description for color space {primaries:BT709, transfer:SRGB, matrix:RGB, range:FULL}
[2:0322/120305.103142:ERROR:ui/ozone/platform/wayland/host/wayland_wp_color_management_surface.cc:63] Failed to get image description for color space.
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