Hey, thanks for the detailed feature request.
We don’t have a full X minimizes to tray behavior yet, but there’s already a partial workaround. Turn on the Show Cursor in system tray setting, it’s enabled by default. After that, clicking the system tray icon will hide and restore the window, while the Cursor process and any running agents stay alive in the background. So the hide window without killing the session behavior already works, it’s just not wired to the X button yet.
An opt-in toggle for the X button, like in Discord or Slack, makes sense. I’ve logged the request. Votes in this thread help us gauge demand, so if any other user needs this, please ask them to drop in and upvote.
Related thread for reference: Hide to System Tray it’s about fully hiding from the taskbar, so it’s a slightly different use case.