I'm able to issue a get-psrepository command without error but still not able to install the requested module.
I've changed the $debugpreference to "Continue" and get a detailed log. I'm not sure but I think the relevant information is :
DEBUG: 00:00:00.0707830 OPTION: Name => Az
VERBOSE: The -Repository parameter was not specified. PowerShellGet will use all of the registered repositories.
VERBOSE: Getting the provider object for the PackageManagement Provider 'NuGet'.
VERBOSE: The specified Location is 'https://www.powershellgallery.com/api/v2' and PackageManagementProvider is 'NuGet'.
DEBUG: 00:00:00.0804809 PackageProvider::FindPackage with name Az
DEBUG: 00:00:00.0836448 Calling 'NuGet'::'FindPackage' - name='Az', requiredVersion='',minimumVersion='', maximumVersion='''.
DEBUG: 00:00:00.0842153 Iterating 'Az'.
DEBUG: 00:00:00.0852100 There are '0' registered sources in 'NuGet' provider.
DEBUG: 00:00:00.0857066 Source 'https://www.powershellgallery.com/api/v2' is not one of the registered sources in 'NuGet' provider.
VERBOSE: An error occurred while sending the request.
VERBOSE: Retry downloading 'https://www.powershellgallery.com/api/v2' for '2' more times
VERBOSE: An error occurred while sending the request.
VERBOSE: Retry downloading 'https://www.powershellgallery.com/api/v2' for '1' more times
VERBOSE: An error occurred while sending the request.
VERBOSE: Retry downloading 'https://www.powershellgallery.com/api/v2' for '0' more times
WARNING: Unable to resolve package source 'https://www.powershellgallery.com/api/v2'.
VERBOSE: Total package yield:'0' for the specified package 'Az'.
DEBUG: 00:00:01.7105453 Completed iterating for 'Az'.
DEBUG: 00:00:01.7116667 PowerShell Script 'PSModule' Function 'Find-Package' returns null.
DEBUG: 00:00:01.7137400 Done calling powershell «Find-Package» «PSModule»
DEBUG: 00:00:01.7144444 unmatched package name='Az'
PackageManagement\Install-Package : No match was found for the specified search criteria and module name 'Az'. Try Get-PSRepository to see all available registered module repositories.
At C:\Program Files\WindowsPowerShell\Modules\PowerShellGet\1.0.0.1\PSModule.psm1:1772 char:21