chore: add TypeScript support

Added TypeScript configuration for Vite and Node (tsconfig.app.json and
tsconfig.node.json, referenced in tsconfig.json).
Vite configuration was migrated to TypeScript.
Added ESLint TypeScript rules and general ESLint TypeScript
configuration.
Npm scripts for type checking have been added and build script has been
updated to run type checking script before building.

vite.config.ts

@@ -0,0 +1,42 @@
+/*
+Copyright 2026 Seekra
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+    http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+*/
+
+import vue from '@vitejs/plugin-vue';
+import { fileURLToPath, URL } from 'node:url';
+import { defineConfig } from 'vitest/config';
+import { createHtmlPlugin } from 'vite-plugin-html';
+
+// https://vite.dev/config/
+export default defineConfig({
+    build: {
+        target: 'es2020',
+    },
+    plugins: [
+        vue(),
+        createHtmlPlugin({
+            minify: true,
+        }),
+    ],
+    resolve: {
+        alias: {
+            '@': fileURLToPath(new URL('./src', import.meta.url)),
+        },
+    },
+    test: {
+        globals: false,
+        environment: 'jsdom',
+    },
+});