chore(react-router): Add library mode E2E test #11240

Job	Run time
check-permissions	1s
Formatting, linting & changeset checks	2m 1s
Integration Tests (generic, chrome)	4m 4s
Unit Tests (18)	41s
Integration Tests (express, chrome)	1m 51s
Unit Tests (22)	44s
Integration Tests (quickstart, chrome)	2m 3s
Integration Tests (ap-flows, chrome)	2m 21s
Integration Tests (elements, chrome)	2m 27s
Integration Tests (sessions, chrome)	3m 26s
Integration Tests (astro, chrome)	2m 47s
Integration Tests (expo-web, chrome)	2m 9s
Integration Tests (tanstack-start, chrome)	3m 30s
Integration Tests (tanstack-router, chrome)	1m 57s
Integration Tests (vue, chrome)	2m 34s
Integration Tests (nuxt, chrome)	2m 16s
Integration Tests (react-router, chrome)	1m 58s
Integration Tests (nextjs, chrome, 13)	5m 31s
Integration Tests (nextjs, chrome, 14)	5m 42s
Integration Tests (nextjs, chrome, 15)	8m 1s
	56m 4s

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