You create a PowerShell session at the beginning of your script. But you never ENTER the session. Your Test-Path is checking the LOCAL machine and your New-Item will create the directory on the LOCAL machine.
The Copy-Item uses the UNC name in the $SourcePath and copies the item to the location found in the $DestinationPath on the machine in your $Session variable ("TestComputer") -- but you're running the Copy-Item on YOUR LOCAL machine, not the remote machine.