Exchange 2013 IIS Backend site recreation

I've been able to restore the Exchange Back End site by copying the applicationHost.config from an auto-created backup located in C:\inetpub\history.
Unfortunately, even if the WebSites tree is now correctly populated in IISAdmin, the Exchange Management Shell still cannot connect to Server.
I've also tried to restore MetaBase.xml with an old copy from C:\Windows\System32\inetsrv\History with no luck...

Created a disk snapshot of the problematic server. Now trying to install Exchange Rollup Update 21 but the installer stops with the following error:
Unable to remove product with code 4934d1ea-be46-48b1-8847-f1af20e892c1. Fatal error during installation. Error code is 1603. Last error reported by the MSI package is 'The specified account already exists.

A similar problem is reported here:
https://social.technet.microsoft.com/Forums/lync/en-US/2c0b5ed3-3b28-414f-ba37-14b059e77830/unable-to-remove-product-with-code-4934d1eabe4648b18847f1af20e892c1?forum=exchangesvrdeploy
but, in fact I don't have any interim update installed.

Tried to run:
MsiExec.exe /X {4934d1ea-be46-48b1-8847-f1af20e892c1}
with no luck...

Create the name of the backend iis site and then remove and create back again the sites
https://theitbros.com/recreate-owa-ecp-virtual-directories-exchange-server-2016/
(that would be my approach) and be careful with the delete button.

Thank you Jose.
Unfortunately I cannot follow your suggestion since Management Shell cannot connect with server and  ExchangeCmdlets are not available in plain Powershell

You're wrong. Plain wrong.

You can open a regular powershell console and use :
for 2010
Add-PSSnapin Microsoft.Exchange.Management.PowerShell.E2010;

or 2013/16/19
Add-PSSnapin Microsoft.Exchange.Management.PowerShell.SnapIn;

And after that, you can use the regular Exchange cmdlets.

Great Jose, thank you for the hint!

Here is the taken actions:
- recreated owa and ecp virtual directories
- restarted IIS
- enabled the following authentication methods for owa (Default site):  Basic, Windows Authentication
- enabled the following authentication methods for ecp (Default site):  Basic, Windows Authentication
- enabled the following authentication methods for owa (Exchange Back End): Anonymous, Windows Authentication
- enabled the following authentication methods for ecp (Exchange Back End): Anonymous, Windows Authentication

The situation is:
- Exchange Management Shell still does not connect
- ecp web page opens but, after authentication, a blank page is loaded
- owa is just blank, no authentication

Maybe I can try to recreate EWS virtual directory in Exchange Backend Site, as explained here:
https://blogs.technet.microsoft.com/get-exchangehelp/2013/02/07/managing-exchange-2013-iis-virtual-directories-web-applications/
but I fear I could do further harm to the system..