So this is at face value simple.
Taking examples from other apps like Discord or Telegram desktop they can auto start (including in app setting), and can hide themselves on the applets/notifications bar, Which let them run unobtrusive and notify you if applicable.
It's just a tiny feature, but I feel it could be a great quality of life feature to implement.
This is a mock-up of what I mean by applet: https://imgur.com/ouj1bsV