"You have much less options when you are processing PowerShell objects."
There is simply no need for the kind of extensive text processing common in Linux because every command returns an object whose fields can be directly referenced. Combined with the ConvertTo-Json command this is incredibly powerful. Honestly it seems like you are attempting to do things in PowerShell the bash way instead of the PowerShell way.
" I think the first thing I tried to do in PowerShell was a script that scanned a directory recursively for files containing a CRC in their name, and then check it"
I wrote a PowerShell script that recursively scanned every filed and folder on our fileshares and wrote the permissions to a file for later indexing.