I have never been able to see the output of TeXmacs on Windows Powershell. But I found out that if one redirects standard output and standard error to file, one can see them. Today it did not work for me with
Start-Process -FilePath "C:\Program Files (x86)\TeXmacs\bin\texmacs.exe" 2>&1 > output_tm.txt
but it worked with
Start-Process -FilePath "C:\Program Files (x86)\TeXmacs\bin\texmacs.exe" -RedirectStandardOutput stdout.txt -RedirectStandardError stderr.txt
stderr.txt is created in the current working directory of Powershell.
I found the commands out with Internet searches, done both some time ago and today. Today I took the command from https://stackoverflow.com/questions/8761888/capturing-standard-out-and-error-with-start-process
Hope that it helps!