Stats bar round 4 (owner): optical spacing — tight to the composer, floating below

The rhythm agreed with the owner: the stats/controls row hugs the
composer (8px — reads as the card's metadata, one object), and the
whole cluster floats with deliberate air above the screen bottom
(20px). The 8px straight-edge gap optically matches the 6px pill-to-
pill gap: two rounded pills' corridor reads wider than geometric, so
rounded-rounded gaps run ~2px tighter than straight-edge gaps.

- stats-bar.tsx: pt-4 -> pt-2 (8px under the composer) — shared by
  chat and home automatically
- chat.tsx dock block + home.tsx composer wrapper: pb-4 -> pb-5

The dock's reserve auto-measures the block, so the spacer/fold
machinery adapts on its own.

components/stats-bar.tsx

@@ -66,7 +66,7 @@ export function StatsBar({
 			// (so its transparent gradient area never blocks scrolling) — this row
 			// must re-enable events or every control on it is dead (the model-
 			// control wave caught this live: buttons rendered, clicks never landed).
-			className="pointer-events-auto relative flex items-center justify-between gap-3 px-3 pt-4 text-xs text-muted-foreground"
+			className="pointer-events-auto relative flex items-center justify-between gap-3 px-3 pt-2 text-xs text-muted-foreground"
 		>
 			{/* The summary button + its popover: the popover anchors to this
 			    wrapper, CENTERED over the button itself (owner, stats round 2)