The normal output of a service is a log, and should go to STDOUT. The service can separately output errors to STDERR.
The normal output of a non-service command (eg. grep) sometimes/often goes to STDOUT, which is why that command will write errors to STDERR -- even "info" messages that look like logging.
dunno if you haven't noticed but people haven't been writing self-daemonizing processes that disappear into the background silently for ::checks watch:: at least a decade now. The practice of writing self-daemonizing processes was always a wart, a reflection of how low our expectations are of the job-control expressivity of cli shells. Grab ten programmers who use bash/zsh every day and say "you have a program that runs in the foreground forever, launch it in the background and close your terminal" and see what they do. You'll find some mixture of nohup, launching it and putting it in the background and disowning it, putting it in a tmux session and then detaching from the session, or deciding they have to put it in a container just to get that behavior, or some other workaround to deal with the fact that launching a process into the background is an ergonomic challenge for a lot of people. The circa-2000 status quo actually had a drawback or two.
