feat(webchat): add slash commands, autocomplete popup, and web search button

Add 6 slash commands (/help, /reset, /compact, /usage, /status, /model)
with autocomplete popup (arrow keys, Enter/Tab/Escape navigation).
Search button toggles web search mode by prepending instruction to message.
Backend agent.send extended with metadata for server-side command routing.

docs/plans/state.json

@@ -962,6 +962,34 @@
       ],
       "test_status": "21/21 passing (html.test) + 18/18 passing (gmail.test) + 16/16 passing (automation/gmail.test)"
     },
+    "webchat-slash-commands": {
+      "status": "completed",
+      "date": "2026-02-10",
+      "summary": "Slash commands, autocomplete popup, and web search button for the webchat SPA. 6 commands: /help, /reset, /compact, /usage, /status, /model. Search button toggles web search mode (prepends instruction to message). Backend agent.send extended with metadata for command routing.",
+      "phases": {
+        "backend_command_handling": {
+          "status": "completed",
+          "description": "Extended agent.send RPC handler to accept optional metadata (isCommand, command). /reset handled server-side via agent.reset().",
+          "files_modified": [
+            "src/gateway/handlers/agent.ts"
+          ]
+        },
+        "frontend_slash_commands": {
+          "status": "completed",
+          "description": "Slash command parsing, autocomplete popup (arrow keys, Enter/Tab/Escape), search button toggle, system messages, /help /reset /compact /usage /status /model handlers",
+          "files_modified": [
+            "src/gateway/ui/pages/chat.js"
+          ]
+        },
+        "css_styling": {
+          "status": "completed",
+          "description": "Styles for .chat-actions, .btn-action, .slash-popup, .slash-popup-item, .message.system, .chat-input-wrapper, plus responsive breakpoints for 600px and 768px",
+          "files_modified": [
+            "src/gateway/ui/style.css"
+          ]
+        }
+      }
+    },
     "tui-fullscreen-improvements": {
       "status": "completed",
       "date": "2026-02-10",