You reach for the stoplights to put the panel away, so here they are, red and green only, on by default to try. Red hides the panel, as ⌘W does. Green floats a docked panel, and docks a floating one. Each header is 380 pt wide. Hover the lights to see their glyphs, and click green on the screen below.
The pair takes 40 pt: two 12 pt buttons, 8 pt apart, and their margins. Today and All tasks still fit at 380 pt. A long project name with the ‹ cuts off sooner, and the empty space you drag shrinks by the same amount.
With the lights at the top left, the ␣⌘ badge beside them makes three marks in a row. Either way About stays in the menu, as it already is. C drops the badge. D drops the badge and the ⋮, and the mark, drawn as the menu bar's Colour glyph, opens the menu at the header's right end. The menu bar mark opens the same menu, so the panel's mark would match it. Click D's mark to open its menu.
On by default, for now. Under the Settings regroup's option B it sits on the new Appearance tab, in Menu bar and Dock. Otherwise in General, after Show in Dock.
14. Should the lights show all the time (A), or only while the pointer is over the header (B)? I recommend A: you reach for them without looking, and macOS already greys them while the panel isn't in front.
15. Should green float a docked panel and dock a floating one, with ⌥ for full height? Yes or no?
16. Should the switch be called "Window buttons"? Yes, or suggest a name.
17. With the lights on, should the header keep the badge (A), drop it (C), or drop the badge and the ⋮ so the Colour mark opens the menu (D)? I lean D: one mark, at the end, doing what the menu bar mark does.
18. With the lights off, should the header go back to the badge and the ⋮ as now? Yes or no?