Add site-wide login gate protecting the whole app

Chat/memory/logs/models APIs were reachable without any auth even
though the app is deployed publicly behind Caddy HTTPS; only the
settings screen had a password. Add an optional SITE_PASSWORD-backed
session cookie gate in front of everything (settings included, on
top of its existing SETTINGS_PASSWORD), with a matching login screen
on the frontend. Stays fully backward compatible: with SITE_PASSWORD
unset the app behaves exactly as before.

Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>

frontend/src/components/LoginGate.vue

@@ -0,0 +1,56 @@
+<script setup lang="ts">
+import { ref } from 'vue'
+import { useAuthStore } from '../stores/auth'
+
+const store = useAuthStore()
+const passwordInput = ref('')
+
+async function submit() {
+  const ok = await store.login(passwordInput.value)
+  if (ok) passwordInput.value = ''
+}
+</script>
+
+<template>
+  <div class="login-gate">
+    <form class="card" @submit.prevent="submit">
+      <span class="title">PlayChat</span>
+      <p class="hint">サイトを利用するにはパスワードが必要です。</p>
+      <input
+        v-model="passwordInput"
+        type="password"
+        placeholder="パスワード"
+        autocomplete="current-password"
+        autofocus
+      />
+      <button type="submit" :disabled="store.loading || !passwordInput">
+        {{ store.loading ? '確認中...' : 'ログイン' }}
+      </button>
+      <p v-if="store.error" class="error">{{ store.error }}</p>
+    </form>
+  </div>
+</template>
+
+<style scoped>
+.login-gate {
+  height: 100vh; display: flex; align-items: center; justify-content: center;
+  background: #111;
+}
+.card {
+  display: flex; flex-direction: column; gap: 10px;
+  width: 280px; padding: 24px; background: #1a1a1a;
+  border: 1px solid #2a2a2a; border-radius: 10px;
+}
+.title { font-size: 18px; font-weight: 600; color: #fff; }
+.hint { font-size: 12px; color: #888; }
+input {
+  background: #2a2a2a; color: #eee; border: 1px solid #444;
+  border-radius: 6px; padding: 8px 10px; font-size: 13px; width: 100%;
+}
+button {
+  background: #1d3557; color: #93c5fd; border: 1px solid #2563eb;
+  border-radius: 6px; padding: 8px 10px; font-size: 13px; cursor: pointer;
+}
+button:disabled { opacity: 0.5; cursor: default; }
+.error { font-size: 12px; color: #f87171; }
+</style>