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.

src/gateway/ui/style.css

@@ -529,6 +529,30 @@ header #status.status-ok {
   .card .value {
     font-size: var(--font-size-lg);
   }
+
+  .chat-layout {
+    height: calc(100vh - 32px);
+  }
+
+  .chat-header {
+    padding-bottom: 8px;
+    margin-bottom: 8px;
+  }
+
+  .btn-action {
+    font-size: 11px;
+    padding: 6px 8px;
+    min-height: 36px;
+  }
+
+  .slash-popup-item {
+    padding: 10px 12px;
+  }
+
+  .slash-popup-item .cmd-name {
+    min-width: 70px;
+    font-size: var(--font-size-sm);
+  }
 }
 
 /* ==========================================================================
@@ -904,6 +928,117 @@ tr:hover td {
   cursor: not-allowed;
 }
 
+/* Chat actions bar (search button, etc.) */
+.chat-actions {
+  display: flex;
+  align-items: center;
+  gap: 8px;
+  padding: 8px 0;
+}
+
+.btn-action {
+  display: inline-flex;
+  align-items: center;
+  gap: 6px;
+  padding: 6px 12px;
+  border-radius: 16px;
+  background: var(--bg-tertiary);
+  color: var(--text-secondary);
+  border: 1px solid var(--border);
+  font-family: var(--font-mono);
+  font-size: var(--font-size-sm);
+  cursor: pointer;
+  white-space: nowrap;
+  user-select: none;
+  transition: all var(--transition);
+}
+
+.btn-action:hover {
+  color: var(--text-primary);
+  border-color: var(--text-muted);
+  background: var(--bg-secondary);
+}
+
+.btn-action.active {
+  background: var(--accent-muted);
+  color: var(--accent);
+  border-color: var(--accent);
+}
+
+.btn-action svg {
+  width: 14px;
+  height: 14px;
+  flex-shrink: 0;
+  fill: currentColor;
+}
+
+/* Slash command autocomplete popup */
+.chat-input-wrapper {
+  position: relative;
+}
+
+.slash-popup {
+  position: absolute;
+  bottom: 100%;
+  left: 0;
+  right: 0;
+  margin-bottom: 4px;
+  background: var(--bg-secondary);
+  border: 1px solid var(--border);
+  border-radius: var(--radius);
+  max-height: 240px;
+  overflow-y: auto;
+  z-index: 100;
+  box-shadow: 0 -4px 16px rgba(0, 0, 0, 0.3);
+}
+
+.slash-popup-item {
+  display: flex;
+  align-items: baseline;
+  gap: 12px;
+  padding: 8px 12px;
+  cursor: pointer;
+  transition: background var(--transition);
+}
+
+.slash-popup-item:hover,
+.slash-popup-item.selected {
+  background: var(--bg-tertiary);
+}
+
+.slash-popup-item .cmd-name {
+  color: var(--accent);
+  font-weight: 600;
+  font-size: var(--font-size-base);
+  min-width: 80px;
+}
+
+.slash-popup-item .cmd-desc {
+  color: var(--text-muted);
+  font-size: var(--font-size-sm);
+}
+
+/* System messages */
+.message.system {
+  align-self: stretch;
+  max-width: 100%;
+  background: var(--bg-tertiary);
+  color: var(--text-secondary);
+  border: 1px solid var(--border-light);
+  font-size: var(--font-size-sm);
+}
+
+.message.system strong {
+  color: var(--text-primary);
+}
+
+.message.system code {
+  color: var(--accent);
+  background: var(--bg-secondary);
+  padding: 1px 4px;
+  border-radius: 3px;
+}
+
 /* Streaming text cursor */
 .streaming-cursor::after {
   content: '|';
@@ -1212,4 +1347,27 @@ tr:hover td {
   .stats-grid {
     grid-template-columns: repeat(2, 1fr);
   }
+
+  .chat-header {
+    flex-wrap: wrap;
+    gap: 8px;
+  }
+
+  .chat-header select {
+    min-width: 0;
+    flex: 1;
+  }
+
+  .chat-actions {
+    padding: 6px 0;
+  }
+
+  .btn-action {
+    padding: 8px 10px;
+    min-height: 36px;
+  }
+
+  .slash-popup {
+    max-height: 200px;
+  }
 }