If you have winget and powershell installed, try `Get-WingetPackage` and see what comes out. Or even better:
gcm | ? noun -like winget*
help Install-WinGetPackage
The "usual" winget cli tool is indeed not powershell compatible. But winget also ships with all the necessary cmdlets. You don't have to install anything extra.
The Winget module is a wreck. The way it is designed, unfortunately, neither fits the object oriented approach of PowerShell nor follows the PowerShell guidelines for cmdlets.
I was super excited to see this comment, but I don't seem to have those cmdlets, even though I'm on Windows 11, fully updated. Are you sure you didn't install something extra?
If I recall correctly, they only work in PowerShell 7. If you don’t even have them in there, you can install them from https://github.com/microsoft/winget-cli (which is bad UX, but if you just need them on one system it’s a way to do it).
I'm in PowerShell 7.4.2 and they're definitely absent. I hadn't thought to install directly from GitHub, given part of the whole shtick of winget is it's The One True Package Manager and bundled, but I can't say I'm surprised, either...