The problem in the end was in the vB Template, where $jsGlobalsfromvB was given after the Vue components were loaded, meaning that vbuserId and vbtheURL were not set at the time the components were rendered.
Not sure if it a good idea to use the userid in the client-side code for security reasons, but it's worth a thought. Since the userid is only used to determine which panel is opened and which icon to show, it might be worth a bit of hacking in the dev console to see how this could be exploited.
Otherwise, the main goal of moving the jQuery to Vue.js has been accomplished (thanks and hats off to Scott for helping) and this demo header component for a navbar is basically done. Next would be to move the navbar menu to a Vue.js component and to also move the panels in the header to Vue components.
Obviously, it is much easier to design a new web site from the beginning with Vue other than trying to retrofit the old site into Vue; but on the other hand, having an existing site to modify does provide opportunities to improve the site along the way.