task_ui: Move status indicator into tab bar of terminal panel (#10846)

I'm not a huge fan of this change (& I expect the placement to change).
The plan is to have the button in a toolbar of terminal panel, but I'm
not sure if occupying a whole line of vertical space for a single button
is worth it; I suppose we might want to put more of tasks ui inside of
that toolbar.
Release Notes:

- Removed task status indicator and added "Spawn task" action to
terminal panel context menu.