Relocates ui/litellm-dashboard/e2e_tests to tests/e2e/ui so all end to end
suites live under tests/e2e. The suite stays in TypeScript and becomes a
self-contained npm package with its own package.json, lockfile and tsconfig
instead of leaning on the dashboard's toolchain; the dashboard drops its
@playwright/test dependency, e2e scripts and knip/vitest/tsconfig carve-outs.
CI paths follow the move: both CircleCI jobs (main e2e and the
SERVER_ROOT_PATH migration smoke) and the test_server_root_path workflow now
install and run Playwright from tests/e2e/ui, with the node cache keyed on
both lockfiles. classify_changes.sh treats tests/e2e/ui as client so spec
edits keep skipping backend jobs. The suite's mock LLM fixture is excluded
from the e2e basedpyright zero-error gate in pyrightconfig.json since it
belongs to the TS suite, not the typed Python harness.
