fix(docs): localize the docs homepage, nav, and sidebar chrome across 20 languages (#547)

Localize the docs homepage (DocsHome.vue), top nav, and sidebar structural labels into all 20 non-English locales; individual tool names stay English by design. Also derive the homepage tool-count chips from the shared catalog via toolSection() so they no longer drift.

apps/docs/.vitepress/theme/section-counts.data.ts

@@ -0,0 +1,21 @@
+// Build-time per-section tool counts for the docs homepage chips. Derived from
+// the shared TOOLS catalog via toolSection() so the numbers never drift (the
+// project's single-source-of-truth rule for per-section counts). Runs in Node
+// during the VitePress build; only the resulting numbers reach the client.
+import { defineLoader } from "vitepress";
+import { TOOLS } from "../../../../packages/shared/src/constants.ts";
+import { type Section, toolSection } from "../../../../packages/shared/src/section.ts";
+
+export type SectionCounts = Record<Section, number>;
+
+declare const data: SectionCounts;
+
+export { data };
+
+export default defineLoader({
+  load(): SectionCounts {
+    const counts: SectionCounts = { image: 0, video: 0, audio: 0, pdf: 0, files: 0 };
+    for (const tool of TOOLS) counts[toolSection(tool)]++;
+    return counts;
+  },
+});