PowershellGet on PS7 is not registered or registerable

[glatzert]

I installed PowerShell 7 and have troubles with PowerShellGet, there seems to be an hen-before-the-egg-problem.

Install-Module <someModule>
# triggers nuget install, which fails with 'Unable to find repository with SourceLocation ''. Use Get-PSRepository to see all available'

Get-PSRepostiery
# fails with 'Unable to find module providers (PowerShellGet)'

Get-PackageSource
# fails with 'Unable to find package providers ().'

Get-PackageProvider -ListAvailabel
# is empty

Install-PackageProvider -Name nuget
# fails with 'Unable to find repository with SourceLocation '''.

Register-PackageSource
# fails with unable to find packageProviders

Is there anything which can be done to RESET the whole OneGet/PowerShellGet experience?
Adding informations from $PSVersionTable

Name                           Value
----                           -----
PSVersion                      7.0.0
PSEdition                      Core
GitCommitId                    7.0.0
OS                             Microsoft Windows 10.0.18362
Platform                       Win32NT
PSCompatibleVersions           {1.0, 2.0, 3.0, 4.0…}
PSRemotingProtocolVersion      2.3
SerializationVersion           1.1.0.1
WSManStackVersion              3.0