The old flex spacer split the header in half, boxing the strip into the
middle while tabs shrank to slivers; the spacer now renders only for
the VS Code and surface-title layouts, tabs keep a fixed width (w-44)
and the strip scrolls behind the right-side buttons. Every tab gains a
hover-revealed close button next to the menu; the active tab's menu is
hover-revealed too (it was always visible) — the header passes it into
the strip so both overlays behave identically. The active tab's inner
padding matches inactive tabs.