chore: remove Playwright end-to-end testing setup

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

package.json

@@ -18,7 +18,6 @@
 		"diag:permissions": "tsx scripts/diagnose-permission-page.ts",
 		"jobs:worker": "node --conditions=react-server --import tsx scripts/jobs-worker.ts",
 		"test": "vitest run",
-		"test:e2e": "playwright test",
 		"typecheck": "tsc --noEmit",
 		"db:generate": "drizzle-kit generate",
 		"db:introspect": "drizzle-kit introspect",
@@ -86,7 +85,6 @@
 	"devDependencies": {
 		"@babel/parser": "7.29.8",
 		"@biomejs/biome": "2.5.12",
-		"@playwright/test": "^1.62.1",
 		"@tailwindcss/forms": "0.5.11",
 		"@tailwindcss/postcss": "4.3.3",
 		"@tailwindcss/typography": "0.5.20",