For some reason the repositories refuse to sync until after I have manually logged in on the dashboard.
This is expected. The user account cannot interact with GitHub until you have gone through the oauth2 login process, which generates an oauth2 access token and refresh token, and authorizes Drone to access data on your behalf.
Under the hood this endpoint makes an API call to github/gitlab/gogs/gitea/bitbucket and requires an access token. This token is only available after a login. It is therefore required to login before you can invoke this endpoint.