feat: add "Hello from the otter side" easter eggs

Custom 404 pages for landing and docs sites, otter greeting on the
first-login sidebar, and a one-time welcome toast after password change.

apps/docs/.vitepress/theme/Layout.vue

@@ -16,5 +16,59 @@ const { Layout } = DefaultTheme;
         <GitHubStars />
       </div>
     </template>
+    <template #not-found>
+      <div class="not-found-page">
+        <span class="not-found-otter">🦦</span>
+        <h1 class="not-found-heading">Hello from the otter side!</h1>
+        <p class="not-found-text">This page swam away. Let's get you back on track.</p>
+        <a href="/" class="not-found-link">Back to docs</a>
+      </div>
+    </template>
   </Layout>
 </template>
+
+<style scoped>
+.not-found-page {
+  display: flex;
+  flex-direction: column;
+  align-items: center;
+  justify-content: center;
+  min-height: 60vh;
+  text-align: center;
+  padding: 2rem;
+}
+
+.not-found-otter {
+  font-size: 4.5rem;
+}
+
+.not-found-heading {
+  margin-top: 1.5rem;
+  font-size: 2.25rem;
+  font-weight: 700;
+  letter-spacing: -0.02em;
+}
+
+.not-found-text {
+  margin-top: 1rem;
+  font-size: 1.125rem;
+  color: var(--vp-c-text-2);
+}
+
+.not-found-link {
+  margin-top: 2rem;
+  display: inline-block;
+  padding: 0.625rem 1.5rem;
+  border-radius: 0.5rem;
+  background: var(--vp-c-brand-1);
+  color: var(--vp-c-white);
+  font-size: 0.875rem;
+  font-weight: 500;
+  transition: background 0.2s;
+}
+
+.not-found-link:hover {
+  background: var(--vp-c-brand-2);
+  text-decoration: none;
+}
+</style>