feat: work-type modes — Talk / Poker / Build / Explore / Study

The manual version of the architecture's `route` step: Brian points her at the
TYPE of work and her register + tools shift to match. Biggest single lever on the
'meh' problem (a mode card can demand decisive/technical/generative, countering
gpt-4o's default warm-vapor).

- modes.py: Build (heads-down engineering — decisive, concrete, tradeoffs, no
  listicles), Explore (open brainstorming — generative, riffs + honest catch,
  spawn threads, don't converge early), Study (poker review away from the table —
  analytical, GTO-aware, teaching; read-only lookups + analyze_spot). Cash relabeled
  Poker (key kept for compat).
- UI: mode selectors (desktop + mobile) get all five; badge taps now cycle modes.
- design: docs/COGNITION.md (the society-of-parts control-plane sketch).
- tests: presence + tool-gating for the new modes. Suite 85, ruff clean.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

lyra/web/static/index.html

@@ -26,7 +26,10 @@
       <h4>Mode</h4>
       <select id="mobileMode">
         <option value="conversation">💬 Talk</option>
-        <option value="poker_cash">♠ Cash</option>
+        <option value="poker_cash">♠ Poker</option>
+        <option value="build">🛠 Build</option>
+        <option value="explore">🔭 Explore</option>
+        <option value="study">📐 Study</option>
       </select>
     </div>
 
@@ -62,11 +65,14 @@
       </button>
       <span class="brand">Lyra</span>
       <span class="brand-dot" id="brandDot" title="Relay status"></span>
-      <button class="mode-badge" id="modeBadge" type="button" title="Tap to toggle Talk / Cash mode">💬 Talk</button>
+      <button class="mode-badge" id="modeBadge" type="button" title="Current mode (tap to cycle)">💬 Talk</button>
       <label for="mode">Mode:</label>
       <select id="mode">
         <option value="conversation">💬 Talk</option>
-        <option value="poker_cash">♠ Cash</option>
+        <option value="poker_cash">♠ Poker</option>
+        <option value="build">🛠 Build</option>
+        <option value="explore">🔭 Explore</option>
+        <option value="study">📐 Study</option>
       </select>
       <button id="settingsBtn" style="margin-left: auto;">⚙ Settings</button>
       <div id="theme-toggle">
@@ -605,8 +611,10 @@
 	}
 
 
-    // ----- Conversation mode (Talk / Cash) -----
-    const MODE_LABELS = { conversation: "💬 Talk", poker_cash: "♠ Cash" };
+    // ----- Conversation modes (Talk / Poker / Build / Explore / Study) -----
+    const MODE_LABELS = { conversation: "💬 Talk", poker_cash: "♠ Poker",
+                          build: "🛠 Build", explore: "🔭 Explore", study: "📐 Study" };
+    const MODE_ORDER = ["conversation", "poker_cash", "build", "explore", "study"];
 
     // Reflect a mode value across the controls + header accent (no network call).
     function applyMode(value) {
@@ -730,8 +738,10 @@
 
       desktopMode.addEventListener("change", (e) => chooseMode(e.target.value));
       mobileMode.addEventListener("change", (e) => { closeMobileMenu(); chooseMode(e.target.value); });
-      modeBadge.addEventListener("click", () =>
-        chooseMode(desktopMode.value === "poker_cash" ? "conversation" : "poker_cash"));
+      modeBadge.addEventListener("click", () => {
+        const i = MODE_ORDER.indexOf(desktopMode.value);
+        chooseMode(MODE_ORDER[(i + 1) % MODE_ORDER.length]);  // tap cycles through modes
+      });
 
       // Reflect the last-used mode immediately; the per-session value loads once
       // the current session is known (below).