I received this error as well. The issue was literally that the web adaptor was unable to reach the URL.
The web adaptor has a URL stored in a WebAdaptor.config file. The usual setup may have this file stored in the following directory:
C:\inetpub\wwwroot\arcgis
IMPORTANT: This directory may be different in your setup, please confirm with your ArcGIS administrator while troubleshooting.
This configuration file has URL entries hard coded into it. (See Below) If one or both of these URLs is/are a mismatch with the URL that the ArcGIS server is set up for, it may result in this error. In my case, the configuration file was accidentally modified manually. Restoring the URL to the correct format (in part by comparing to another functional server) resolved the error and restored access to ArcGIS Server Manager.
IMPORTANT: This is not a declaration that this is the precise issue in your case, but rather an explanation of what I found in mine. If possible, please explore this option with Esri Support to ensure that any trouble-shooting steps taken are supported. Also, before making any edits to any configuration files, ensure that the configuration file in question has been preserved in a backup.
SAMPLE:
<GISServer>
<Nodes>
<Node>someonesserver.organization.com</Node>
</Nodes>
<SiteUrl>https://someonesserver.organization.com:6443</SiteUrl>
I hope this helps! Good luck!
