feat: add GitHub stars button to docs navbar and fix footer license

Add a star button with live count from the GitHub API in the top-right
of the docs site. Fix footer from "MIT License" to "AGPLv3 License".

apps/docs/.vitepress/theme/GitHubStars.vue

@@ -0,0 +1,46 @@
+<script setup lang="ts">
+import { ref, onMounted } from "vue";
+
+const stars = ref<string | null>(null);
+const repo = "https://github.com/stirling-image/stirling-image";
+
+onMounted(async () => {
+  try {
+    const res = await fetch("https://api.github.com/repos/stirling-image/stirling-image");
+    if (!res.ok) return;
+    const data = await res.json();
+    const count = data.stargazers_count;
+    stars.value = count >= 1000 ? `${(count / 1000).toFixed(1)}k` : String(count);
+  } catch {
+    // Silently fail - stars badge just won't show a count
+  }
+});
+</script>
+
+<template>
+  <div class="github-stars-wrapper">
+    <a :href="repo" target="_blank" rel="noopener" class="github-stars-btn">
+      <svg
+        width="16"
+        height="16"
+        viewBox="0 0 16 16"
+        fill="currentColor"
+        aria-hidden="true"
+      >
+        <path
+          d="M8 .25a.75.75 0 0 1 .673.418l1.882 3.815 4.21.612a.75.75 0 0 1 .416 1.279l-3.046 2.97.719 4.192a.75.75 0 0 1-1.088.791L8 12.347l-3.766 1.98a.75.75 0 0 1-1.088-.79l.72-4.194L.818 6.374a.75.75 0 0 1 .416-1.28l4.21-.611L7.327.668A.75.75 0 0 1 8 .25z"
+        />
+      </svg>
+      <span>Star</span>
+    </a>
+    <a
+      v-if="stars !== null"
+      :href="`${repo}/stargazers`"
+      target="_blank"
+      rel="noopener"
+      class="github-stars-count"
+    >
+      {{ stars }}
+    </a>
+  </div>
+</template>