Joining Google Groups
In order to sign in to Wayne OS by Google account, please add your Google account to google-browser-signin-testaccounts@chromium.org.
Then, sign in with your Google account in Wayne OS.
Note
Above method is for test purpose and managed by Google officially.
However, It doesn’t mean that you can use all of Google services since Google restricts/controls third-parties of open source.
Reference
https://wayne-os.com/googles-restriction-for-chromium-chromium-os
https://www.chromium.org/developers/how-tos/api-keys