For this I propose have this SPI methods:

InputStream StartServer.getServerOutput(Target target);
InputStream StartServer.getServerError(Target target);

Server life-cycle implementation need to drain these input stream into
an IDE output tab when starting the server.
Server instance node will have 'Show Output Window' action to bring up
this output tab.

The design is to remove this generic functionality from j2eeserver.
Server plugin could use ProcessExecutor to execute java command and
handle output/error redirection.  Or, plugin could implement its own
CopyMaker for special needs like looking of some error string in the
process input stream.

Based on the above points, I will close this request as won't fix.