Can I customise the connection screen layout?

You can customise the widget's end screens by passing auth_success_redirect_url and auth_failure_redirect_url in the /auth/generateWidgetSession body, sending…

You can customise the widget's end screens by passing auth_success_redirect_url and auth_failure_redirect_url in the /auth/generateWidgetSession body, sending users to your own pages after the flow completes or fails.

The widget's internal layout itself is not freely customisable, but you control which providers appear and where users land afterwards. See customising authentication redirects.