Hello Mark,
In regards to your question, ArcGIS Server Manager should automatically open after upgrading ArcGIS Server by attempting to install the newer version. Once opening Server Manager, you should be prompted with a single button to "Continue Server Upgrade." You should indeed complete this step prior to configuring your new web adaptor.
In regards to logging in to Server, you can do this prior to configuring the new web adaptor (via machinename.domain.com:6443/arcgis). However, you will indeed need to configure the new web adaptor prior to attempting to log in via the URL the web adaptor is configured for (and the URL your services are referenced as in Portal).
ArcGIS Server Upgrade Documentation (see step 6)
Once authorized, ArcGIS Server Manager automatically opens. Click Continue Server Upgrade to complete the upgrade. You must use ArcGIS Server Manager on the local machine where you're running the upgrade to complete this step. You cannot Continue Server Upgrade through a Web Adaptor or load balancer.
To summarize,
If you have gotten past the "Continue Server Upgrade" prompt in the browser, you are good to go in configuring the new web adaptor. If you are still trying to access Server Manager to complete this step, please let us know what error you are getting in the browser.
Hope this helps!
Travis