feat: off the record mode (OTR)

Adds a third input mode toggle alongside Note and Agent. When active:
- Textarea gets a subtle purple tint with dashed border
- OTR button highlights purple
- Placeholder reads "Off the record — not logged or distilled…"
- off_record=True is sent to /chat; session_logger is skipped
- In-memory session context is preserved within the session

Switching to Note or Agent mode deactivates OTR, and vice versa.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

cortex/static/style.css

@@ -571,6 +571,27 @@
         #note-btn.active         { border-color: rgba(180, 130, 40, 0.6); color: #c9a84c; }
         #note-btn.active.public  { border-color: rgba(40, 170, 150, 0.6); color: #4abfb0; }
 
+        /* OTR button */
+        #otr-btn {
+            background: var(--bg);
+            border: 1px solid var(--border);
+            color: var(--muted);
+            border-radius: 8px;
+            padding: 8px 0;
+            cursor: pointer;
+            font-size: 0.85rem;
+            text-align: center;
+            transition: border-color 0.15s, color 0.15s;
+        }
+        #otr-btn:hover        { border-color: var(--muted); color: var(--text); }
+        #otr-btn.active       { border-color: rgba(120, 80, 160, 0.6); color: #a87fd4; }
+
+        /* OTR textarea styling */
+        #input.otr-mode {
+            border-color: rgba(120, 80, 160, 0.4);
+            background: rgba(120, 80, 160, 0.04);
+        }
+
         /* Send button */
         #send {
             background: var(--user-bg);