feat: upgrade to Next.js 15, React 19, and migrate to ESLint 9 flat config

Major framework upgrades:
- Next.js 13 → 15.5.6
- React 18.2.0 → 19.2.0
- ESLint 8 → 9 with flat config migration

Dependency updates:
- @headlessui/react, date-fns, zod, true-myth, usehooks-ts
- @typescript-eslint packages to v8
- TypeScript to v5.9.3
- Prettier to v3.6.2

Breaking changes:
- Migrate from .eslintrc.json to eslint.config.mjs
- Remove deprecated swcMinify option from next.config.mjs
- Update all React type definitions

eslint.config.mjs

@@ -0,0 +1,76 @@
+import typescriptEslint from "@typescript-eslint/eslint-plugin";
+import tsParser from "@typescript-eslint/parser";
+import path from "node:path";
+import { fileURLToPath } from "node:url";
+import js from "@eslint/js";
+import { FlatCompat } from "@eslint/eslintrc";
+
+const __filename = fileURLToPath(import.meta.url);
+const __dirname = path.dirname(__filename);
+const compat = new FlatCompat({
+  baseDirectory: __dirname,
+  recommendedConfig: js.configs.recommended,
+  allConfig: js.configs.all
+});
+
+export default [
+  // Base configuration with ignores
+  {
+    ignores: [
+      ".next/**",
+      "node_modules/**",
+      "out/**",
+      "*.config.mjs",
+      "*.config.js",
+      "next-env.d.ts"  // Next.js generated file
+    ],
+  },
+
+  // Next.js core web vitals using FlatCompat
+  ...compat.extends("next/core-web-vitals"),
+
+  // TypeScript recommended rules
+  ...compat.extends("plugin:@typescript-eslint/recommended"),
+
+  // Base TypeScript configuration
+  {
+    plugins: {
+      "@typescript-eslint": typescriptEslint,
+    },
+
+    languageOptions: {
+      parser: tsParser,
+      ecmaVersion: "latest",
+      sourceType: "module",
+      parserOptions: {
+        project: "./tsconfig.json",
+      },
+    },
+
+    rules: {
+      "@typescript-eslint/consistent-type-imports": "warn",
+    },
+  },
+
+  // Additional strict TypeScript rules for .ts and .tsx files
+  {
+    files: ["**/*.ts", "**/*.tsx"],
+    ...compat.extends("plugin:@typescript-eslint/recommended-requiring-type-checking")[0],
+
+    languageOptions: {
+      ecmaVersion: "latest",
+      sourceType: "module",
+      parserOptions: {
+        project: "./tsconfig.json",
+      },
+    },
+  },
+
+  // Allow CommonJS require in .cjs files
+  {
+    files: ["**/*.cjs"],
+    rules: {
+      "@typescript-eslint/no-require-imports": "off",
+    },
+  },
+];