chore: remove Playwright end-to-end testing setup

Remove Playwright config, e2e spec, dependencies, and related references from package.json, tsconfig.json, and .gitignore.

e2e/smoke.spec.ts

@@ -1,13 +0,0 @@
-import { expect, test } from "@playwright/test";
-
-test("health endpoint is reachable", async ({ request }) => {
-	const res = await request.get("/api/health");
-	expect(res.ok()).toBeTruthy();
-	const body = await res.json();
-	expect(body).toHaveProperty("status");
-});
-
-test("homepage renders", async ({ page }) => {
-	await page.goto("/");
-	await expect(page).toHaveTitle(/.+/);
-});