CmdExec Powershell Job Step Escape Double Quotes
I believe the problem you're having has to do with SQL Server Agent Tokens as referred to by this Stack Exchange post SQL Agent - PowerShell step “syntax error”

Excerpting from that post


  This is a not very intuitive and I was never able to find anything
  concrete on the explanation [e.g. no exact BOL or white paper was
  found]. The syntax error in the SQL Agent job is a T-SQL syntax error
  based on User Tokens. So that basically means that a PowerShell
  Sub-Expression Operator is treated as a Token to SQL Server Agent. So
  in PowerShell this $( ) appears to be treated as reserved character
  sequence for SQL Server Agent.


Referencing your attempts, 

$(get-date -f yyyy-MM-dd).zip


notice the $( where you're trying to get the current date for the zip file.  That syntax is a Powershell sub-expression. This part is attempting to be interpreted by the SQL Server Agent as a token.

My suggestion would be to separate out the sub-expression into another Powershell variable ($ZipDate) first and then use that to finish the Powershell command.

Try this:

powershell.exe "$ZipDate = (get-date -f yyyy-MM-dd); Compress-Archive -Path "C:\TestCompress" -DestinationPath "c:\TestCompressOut\$ZipDate.zip" -CompressionLevel Optimal"