You may process STDOUT and STDERR with separate programs via the next trick:
(test | findstr /N /A:2A "^" ) 2>&1 1>&3 | findstr /N /A:4E "^"
Previous line show STDOUT output preceded by green numbers and STDERR output preceded by red ones. Just use your TEE program instead findstr...
If you have not an adequate TEE program for Batch files, you may find one here: Displaying Windows command prompt output and redirecting it to a file