JeanRG: I went to my PS account and deactivated two-factor authentication and it worked right after attempting to delete the plugin like 5 times. Maybe the GOG client can't use two-factor?
Two factor authentication isn't the real problem here, more a server side security measure, because Galaxy is using some unrecognised (old) browser.
Anyway you can press "Trouble with login?" and then the arrow button (previous page), to continue with the login without any trouble.
More in depth explanation:
https://www.gog.com/forum/general_beta_gog_galaxy_2.0/playstation_connection_timed_out/post581
