Considering that you are passing the $computer variable into the web request, this can be run as a local command and does not need to be run on the target computer, so I would focus on running it as a local command for the moment. I know you said it returns exit code 1, but what is returned in the ‘Local Command Output Log’ column?
I am able to run all of the following commands successfully in BatchPatch as local commands. Obviously I am unable to test your particular web application, so I couldn’t comment on why it would not be doing what you are expecting, but BatchPatch appears to be able to successfully execute invoke-webrequest powershell commands without any issues for me:
powershell.exe -ExecutionPolicy Bypass -command “Invoke-WebRequest https://mysite.whatever”
powershell.exe -ExecutionPolicy Bypass -command “Invoke-WebRequest ‘https://mysite.whatever'”
cmd.exe /c echo . | powershell.exe -ExecutionPolicy Bypass -command “Invoke-WebRequest https://mysite.whatever”
cmd.exe /c echo . | powershell.exe -ExecutionPolicy Bypass -command “Invoke-WebRequest ‘https://mysite.whatever'”