the flatpak install of edge is missing a config file. once this file is added, copilot will work. copilot is an essential part of why people use edge.
dont feel bad, other edge installers for linux also somehow do not include this file in the config
the file that is missing is called HubApps, and it can be copied from any edge install, on windows it would be here:
AppData/Local/Microsoft/Edge/User Data/Default/HubApps
this file needs to be copied to
.var/app/com.microsoft.Edge/config/microsoft-edge/Default/
and restart edge, then copilot will work.
link to sample HubApps file
https://controlc.com/565dfd65