Unfortunately, this WebChat widget capability is not supported with Genesys Cloud.
It is/was meant for Genesys Engage Chat (chat with other platform), allowing to set an "Authorization" header with a custom/configured value (only "Authorization" was allowed as header name - in window._genesys.widgets.main.header).
With Genesys Cloud Chat v2, the Authorization header is used to carry the JWT obtained as the result of the create chat request.
So it can't be overridden with another custom value.