Call Powershell command string from Sql Query Publish profile script
If you turn on SQLCMD mode (from the SSMS Query menu), you can use SQLCMD commands within an SSMS query window. A line beginning with !! will execute the text that follows as an OS command on the client. For example:

!! Powershell -Command "Write-Host ('This message is from PowerShell running on machine ' + $env:COMPUTERNAME)"


The command will similarly be executed when the script is run with the SQLCMD command-line utility with this technique.

Note that the "script string" mentioned in your question will need to be hard-coded in the T-SQL script.