Many users experience a problem when they want to link Health Sync with their Fitbit account, using the Google signin, required after you upgraded the Fitbit account to a Google account. This happens since September 16. We reported it to Fitbit and they are looking into it. The same problem can occur when you want to connect another app with Fitbit. It is not a Health Sync issue, but a Fitbit/Google issue. But there is a workaround!
You can easily solve this, but it requires a few actions.
In the Google account selection screen where you can’t select your Google account, please click on three dots menu in the top right corner, and then click on the refresh button:

After you do this, you can select your Google account for Fitbit in the Google account selection screen.
We hope that Fitbit solves this issue soon.