Oddly, emacs-server doesn’t seem to have an option to write a PID file when it starts up. Here’s some ELisp you can drop into your init file to make it happen:
May I write to you? From time to time I'll send you a SIGAVDI newsletter with a few handpicked links, an update on what I've published lately, and some reflections at the intersection of code and life. Replies go directly to me, and I do my best to respond to every single one.