feat(blog): add file-based blog with dynamic slugs, MDX content and layout shell

- Introduced blog routing using Next.js App Router
- Implemented dynamic [slug] pages for blog posts
- Added MDX-based content loading via lib/posts
- Integrated shared TopBar layout with navigation
- Established clear content, lib and component separation

apps/public-web/lib/posts.ts

@@ -0,0 +1,55 @@
+import fs from "fs";
+import path from "path";
+import matter from "gray-matter";
+
+export type PostMeta = {
+    title: string;
+    date: string;
+    excerpt?: string;
+};
+
+export type Post = {
+    slug: string;
+    meta: PostMeta;
+    content: string;
+};
+
+const POSTS_DIR = path.join(process.cwd(), "content", "posts");
+
+function filenameToSlug(filename: string): string {
+    // "2026-01-21-first-post.mdx" -> "first-post"
+    const withoutExt = filename.replace(/\.mdx?$/, "");
+    const parts = withoutExt.split("-");
+    // first 3 parts are date (YYYY-MM-DD), rest is slug
+    return parts.slice(3).join("-");
+}
+
+export function getAllPosts(): Post[] {
+    if (!fs.existsSync(POSTS_DIR)) return [];
+
+    const files = fs.readdirSync(POSTS_DIR).filter((f) => f.endsWith(".mdx") || f.endsWith(".md"));
+
+    const posts = files.map((filename) => {
+        const fullPath = path.join(POSTS_DIR, filename);
+        const raw = fs.readFileSync(fullPath, "utf8");
+        const { data, content } = matter(raw);
+
+        const slug = filenameToSlug(filename);
+
+        const meta: PostMeta = {
+            title: String(data.title ?? slug),
+            date: String(data.date ?? "1970-01-01"),
+            excerpt: data.excerpt ? String(data.excerpt) : undefined
+        };
+
+        return { slug, meta, content };
+    });
+
+    posts.sort((a, b) => (a.meta.date < b.meta.date ? 1 : -1));
+    return posts;
+}
+
+export function getPostBySlug(slug: string): Post | null {
+    const posts = getAllPosts();
+    return posts.find((p) => p.slug === slug) ?? null;
+}