If you’re using PowerShell 7.4 in Windows Terminal (or any terminal application that supports the OSC52 ANSI escape sequence), the Set-Clipboard cmdlet does support piping remote output to the local clipboard via the -AsOSC52 parameter.

You can even configure your PowerShell profile to automatically identify when you’re in a remote shell to automatically apply that parameter without you specifying it.

Set-Clipboard Documentation: https://learn.microsoft.com/en-us/powershell/module/microsoft.powershell.management/set-clipboard?view=powershell-7.4

GitHub Issue that suggested the feature: https://github.com/PowerShell/PowerShell/issues/18116