Nephilim983: Ok, so I'm not a coder/programer but i managed to fix it for myself by trial and error. t's not a perfect streamlined solution so do it at your own risk.

Open Users/"User name"/AppData/Local/GOG.com/Galaxy/plugins/installed/origin_xxxxx/plugin.py in Notepad. Replace lines 38-47 with following:

AUTH_PARAMS = {
"window_title": "Login to EA Play",
"window_width": 495 if is_windows() else 480,
"window_height": 746 if is_windows() else 708,
"start_uri": "https://accounts.ea.com/connect/auth"
"?response_type=code&client_id=EADOTCOM-WEB-SERVER&display=junoWeb/login"
"&locale=en_US&release_type=prod"
"&redirect_uri=https://www.ea.com/ea-play",
"end_uri_regex": "https://www.ea.com/ea-play"
}

This will allow you to log in with a small caveat, Login window won't close. To complete login, just click on EA Play logo at top of the window page. The window will close, and the connection will be established.

Let me know if this works for you or if you can fix my code to automatically close the login window. Good luck.

Tygerboi: Steam
---------

I have found - on different PCs and after reinstalling Windows - that the following process consistently works for me to enable Steam integration / sync in GOG Galaxy:

Browse to the following web site:

https://github.com/ABaumher/galaxy-integration-steam/releases

Download the "windows.zip" file (current version at time of writing this is v1.8)
Navigate to where GOG stores the steam plugin.
%LocalAppData%\GOG.com\Galaxy\plugins\installed\steam_ca27391f-2675-49b1-92c0-896d43afa4f8
If the folder does not exist, create it. If it does, delete everything inside it.
Extract the zip file so all the contents are in that folder.
Start GOG Galaxy.
Connect to Steam in the Settings --> Integrations menu. It should now work properly and you will be authenticated. The plugin version will be v1.0.8.0.

Thanks to ABaumber for this fix.

EA / Origin
---------------

Thanks to GOG users Nephilim983 and MazokuRanma for providing the fix for this (see the screenshot that MazokuRanma uploaded for the fixed/correct syntax, as this messaging forum slightly corrupted it when it was pasted directly into the comments).

https://www.gog.com/forum/general_beta_gog_galaxy_2.0/origin_ea_play_plugin_doesnt_work/page2

This worked for me straight away. Hopefully you will enjoy success as well. :-)