Support "hide taskbar icon"

# Description of the new feature/enhancement

I'd like an option to always hide the taskbar icon, which would often be used with "Always display an icon in the notification area". This frees up taskbar space for those of us who always use global summon or Quake mode.

# Proposed technical implementation details (optional)

[ConEmu](https://github.com/Maximus5/ConEmu) source should have the API call somewhere, per its setting: General > Task bar > Taskbar buttons > Don't show ConEmu window on Taskbar.

Perhaps the setting would look like this, but open to suggestions:

Start by reviewing the existing Windows Terminal settings and code paths for taskbar and notification-area behavior, then compare them with ConEmu's "Don't show ConEmu window on Taskbar" setting. Done means an option can keep the taskbar icon hidden while retaining the notification-area icon, with the behavior working alongside global summon or Quake mode.

Written by the indexing model from the issue text.