Hi @dirkdigs ,
What't the version of the Exchange server?
Could you connect the Exchange management shell in on-premises Exchange server normally?
According to my research on the error information you provided, I found there are many reason could caused this error.
1.Please check the Windows Remote Management (WS-Management) service are running, you could also try to restart this service.
2I see you mentioned that you have checked IIS and checked the bindings for hostnames. What is your configuration? Please right-click Default Web Site, and then click Edit Bindings. If a binding exists for HTTP, clear the host name value.If no binding exists for HTTP, create a new binding that has no host name and a value of All Unassigned for the IP address. Finally restart the IIS.
3.The following is the authentication method of Powershell in "Default Web Site" and "Exchange Back End" in IIS.
4I did some research on similar cases and found that this issue can be caused by having IPv6 enabled on the server. Please try to following the article to set prefer IPv4 over IPv6.
Please refer to: Guidance for configuring IPv6 in Windows for advanced users
In addtion, whether there is a firewall in the environment. If it exists, please make sure that ports 5986 and 5985 have been opened, and the policy set by the firewall will not prevent normal communication.
For more informaiton: Installation and configuration for Windows Remote Management
There is a similar case you could refer to: The WInRM client sent a request to an http server and got a response saying the requested http url was not availabe.
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