feat(tui): put the kawaii face+verb ticker in the status bar, not the thinking panel

The status bar was showing stale lifecycle text ("running…") while the
face+verb stream flickered through the thinking panel as Python pushed
thinking.delta events. That's backwards — the face ticker is the
primary "I'm alive" signal, it belongs in the status bar; the thinking
panel is for substantive reasoning and tool activity.

Status bar now reads `ui.busy`: when true, renders a local `<FaceTicker>`
cycling FACES × VERBS on a 2.5s interval, unaffected by server events.
When false, the bar shows the actual status string (ready, starting
agent…, interrupted, etc.).

Side effect: `scheduleThinkingStatus` still patches `ui.status` with
Python's face text, but while busy the bar ignores that string and uses
the ticker instead. No server-side changes needed — Python keeps
emitting thinking.delta as a liveness heartbeat, the TUI just doesn't
let it fight the status bar.

tui_gateway/server.py

@@ -316,6 +316,8 @@ def resolve_skin() -> dict:
             "branding": skin.branding,
             "banner_logo": skin.banner_logo,
             "banner_hero": skin.banner_hero,
+            "tool_prefix": skin.tool_prefix,
+            "help_header": (skin.branding or {}).get("help_header", ""),
         }
     except Exception:
         return {}