You can never update Windows PowerShell installations on demand - except, in the past, if you upgraded to a new major version, but v5.1 is the last version that will ever be released, given that Windows PowerShell is in maintenance-only will see no new development, unlike its successor, the cross-platform PowerShell (Core) 7+ edition.[1]
Revisions of v5.1 are delivered as part of Windows updates.
However, you can selectively update the PowerShellGet module, in which the problem-causing Register-PSRepository command is defined:
While you normally would just run Update-Module PowerShellGet, a different approach is required the first time, when switching from the bundled PowerShellGet module to the latest version from the PowerShell Gallery:
Open an elevated session (Run as Administrator).
Execute the following (add -Verbose to get detailed information):
Install-Module PowerShellGet -Force
The -Force is to enable installation even though a module by that name is already installed; you may still see a prompt about downloading the NuGet package provider.
Note that the old PowerShellGet version will linger in a different location, but the new one will take precedence over it.
After this initial switch to the gallery-installed version, you'll be able to use
Update-Module PowerShellGet for future versions.
You can use the Get-Command cmdlet to discover a given command's module of origin; e.g.:
PS> (Get-Command Register-PSRepository).Module
ModuleType Version PreRelease Name ExportedCommands
---------- ------- ---------- ---- ----------------
Script 2.1.4 PowerShellGet {Find-Command, Find-DscResource, Find-Module, Find-RoleCapability…}
[1] PowerShell (Core) 7+ versions can be updated on demand - however, as of v7.1, PowerShell [Core] doesn't come with Windows and requires manual installation. However, you can now install and update it via the Microsoft Store application.