I am experiencing this issue as well on Pop!_OS 19.10.
I asked the Pop!_OS developers about it via the General discussion thread on their MatterMost chat (https://chat.pop-os.org), here is what they said:
It happens every now and then. You have to wait until Google re-enables GNOME's API keys. It's referring to GNOME's API key, so it's an issue they often have with GNOME's account.
So basically: "wait until you can log in again." It doesn't sound like there is much that end users can do.
I wonder if it relates to the upgrade cycle, with too many people upgrading to 19.10 at once, and the volume of new sign-ins triggering some flags with the GNOME API KEY? I am usually a "late upgrader" which may be why I never experienced this issue before.
If so, this might be worth a GNOME bug report, as many people upgrading their OS at the same time, which creates a flood of new app sign-ins, should not trigger an app review, IMO. But it also might just be part of Google's standard security process. An inquiry into the developers of Gnome Online Accounts might provide some more info on what to do to fix or prevent this: https://gitlab.gnome.org/GNOME/gnome-online-accounts/
UPDATE: according to https://gitlab.gnome.org/GNOME/gnome-online-accounts/issues/42#note_642763
Hello to the folks that are experiencing this Issue. We're aware about the problem and we (Foundation & respective maintainers) are already working on a solution, as you can see we initially raised this Issue 9 months ago.
In order to keep the thread clean and make the Issue readable to the proper contributors, I'm going to lock this Issue to Contributors only.
I submitted a question about preferred Google account security settings for end users: https://www.reddit.com/r/gnome/comments/dtk2mn/gnome_online_accounts_preferred_login_settings/ just for the sake of thoroughness, just to make sure there isn't something that end users can do to help avoid or resolve the issue. This issue is probably frustrating hundreds or thousands of people.