feat(cli): add guide icon validation and warnings in sync script

apps/cli/sync.ts

@@ -27,7 +27,9 @@
  *   problem page links to it. A guide may be filed into a category `(group)`
  *   folder (e.g. `guides/(2-algorithms)/`) — no route segment, so
  *   `/guides/<slug>` holds — and is found there by slug; a new placeholder
- *   lands at the `guides/` root for a human to file (and give an `icon:`).
+ *   lands at the `guides/` root for a human to file (and give an `icon:`,
+ *   which every badge linking to the guide shows; sync warns while one is
+ *   missing or shared).
  *
  * The sidebar group is the campaign TOPIC from the README table (`tree-dfs/`,
  * ordered by topic number via a script-owned `meta.ts`). A problem outside the
@@ -777,15 +779,21 @@ for (const tag of guideTags) {
 // tag has no landing (`tagTarget()`). A guide whose tag a landing has since
 // claimed has no backlinks left. Counts move with every solved problem, so the
 // badge is rewritten whenever it differs; the rest of the guide is untouched.
-// The same pass warns when a guide's hand-picked `icon:` is one a topic group
-// owns (`TOPIC_ICONS`), so a guide row never reads as a topic row.
+// The same pass checks each guide's hand-picked `icon:`, which is also the icon
+// on every problem-page badge linking to the guide: it must exist, must not be
+// a topic group's (`TOPIC_ICONS`), so a guide badge never reads as a topic's,
+// and must not be another guide's.
 const topicIcons = new Set(Object.values(TOPIC_ICONS));
+const guideIcons = new Map<string, string>(); // icon -> the guide that took it first
 for await (const rel of new Bun.Glob("guides/**/*.mdx").scan(DOCS)) {
   const slug = basename(rel, ".mdx");
   const count = TOPIC_LANDINGS[slug] ? 0 : (tagged.get(slug) ?? 0);
   const page = await Bun.file(join(DOCS, rel)).text();
   const icon = page.match(/^---\n[\s\S]*?\n---/)?.[0].match(/^icon: (\S+)$/m)?.[1];
-  if (icon && topicIcons.has(icon)) console.warn(`${rel}: icon ${JSON.stringify(icon)} is a topic's (TOPIC_ICONS); pick another`);
+  if (!icon) console.warn(`${rel}: no icon; its badges render without one — file it and add \`icon:\``);
+  else if (topicIcons.has(icon)) console.warn(`${rel}: icon ${JSON.stringify(icon)} is a topic's (TOPIC_ICONS); pick another`);
+  else if (guideIcons.has(icon)) console.warn(`${rel}: icon ${JSON.stringify(icon)} is ${guideIcons.get(icon)}'s too; pick another`);
+  else guideIcons.set(icon, rel);
   const next = withBacklinkBadge(page, count);
   if (next === page) continue;
   await Bun.write(join(DOCS, rel), next);