feat: brand UI with real APEX logo + auto-running showcase demo

UI:
- Embed the real APEX logo PNG (transparent mark) in dashboard sidebar,
  cmd-header, landing nav, and landing hero (replaces SVG approximations).
- Add favicon.png across all six templates.
- Nudge color palette to brand cyan→blue→purple gradient and silver-white
  wordmark; word-by-word coloring on the cmd-header tagline.
- Drop-shadow glow on logo marks tuned to the brand-blue.

Demo:
- python -m demo.run_demo now defaults to an auto-running showcase: opens
  the dashboard, kicks off a ~3-4 min optimization that exercises every
  phase, and lands on a verdict modal — no manual setup needed.
- Tight per-iteration targets so Phase 2 actually iterates (visible AI loop).
- Skip per-run AI analysis during Phase 1 exploration via APEX_DEMO_SKIP_PHASE1_AI=1
  to keep total runtime down without losing the headline AI loop in Phase 2.
- --quick flag opts back to the original fast/manual flow.
- --loop auto-restarts for unattended screen recording.

Docs:
- README + SUBMISSION updated to describe the new auto-running default.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

optimizer/pipeline.py

@@ -898,11 +898,17 @@ class OptimizationPipeline:
         delay = float(os.environ.get("APEX_DEMO_RUN_SECONDS", "1.5"))
         time.sleep(max(0.05, delay))
 
-        # Run AI reasoning if enabled — same flow as live mode
-        try:
-            self._reason_about_run(run_id, metrics, [], params)
-        except Exception:
-            pass
+        # Run AI reasoning if enabled — same flow as live mode.
+        # In showcase mode (APEX_DEMO_SKIP_PHASE1_AI=1) we skip Phase 1's
+        # per-run AI analysis to keep total runtime to ~3-4 min. The AI loop
+        # in Phase 2 — where reasoning actually drives parameter changes — is
+        # untouched, so the headline feature is still visible.
+        skip_p1_ai = os.environ.get("APEX_DEMO_SKIP_PHASE1_AI", "").strip() in ("1", "true", "yes")
+        if not (skip_p1_ai and phase.startswith("phase1")):
+            try:
+                self._reason_about_run(run_id, metrics, [], params)
+            except Exception:
+                pass
 
         return ranker.make_result(run_id, params, phase, metrics)