feat(chat): Add Clear button to history popup

Lets you wipe all saved conversations from localStorage (not just
today's) after a confirmation prompt.

chat/index.html

@@ -247,6 +247,22 @@
             .history-item:hover {
                 background: var(--hover-bg);
             }
+            .clear-history-btn {
+                display: block;
+                width: 100%;
+                margin-top: 0.5rem;
+                padding: 0.3rem;
+                background: var(--bg-secondary);
+                color: var(--text-primary);
+                border: 1px solid var(--border-color);
+                border-radius: 0.3rem;
+                font-size: 0.9em;
+                cursor: pointer;
+                transition: background-color 0.2s;
+            }
+            .clear-history-btn:hover {
+                background: var(--hover-bg);
+            }
             .history-time {
                 font-weight: 700;
                 color: var(--text-secondary);
@@ -360,6 +376,9 @@
                                 <span class="history-excerpt" x-text="getExcerpt(item.messages)"></span>
                             </div>
                         </template>
+                        <template x-if="historyItems.length > 0">
+                            <button class="clear-history-btn" @click="clearHistory">Clear</button>
+                        </template>
                     </div>
                 </details>
             </div>
@@ -526,6 +545,12 @@
                     this.$refs.historyPanel.removeAttribute("open");
                     this.scrollToBottom();
                 },
+
+                clearHistory() {
+                    if (!confirm("Clear all saved conversations?")) return;
+                    this.historyItems = clearAllHistory();
+                    this.$refs.historyPanel.removeAttribute("open");
+                },
             });
 
             function attachCopyButtons($el) {
@@ -767,6 +792,11 @@
                 return all[today];
             };
 
+            const clearAllHistory = () => {
+                localStorage.removeItem(STORAGE_KEY);
+                return [];
+            };
+
             document.addEventListener("alpine:init", () => {
                 Alpine.data("chatApp", chatApp);
             });