refactor(ui): extract auth state into AuthContext (#28910)

* refactor(ui): extract auth state into AuthContext

Move auth state (token, userID, userRole, accessToken, premiumUser, userEmail,
disabledPersonalKeyCreation, showSSOBanner) out of src/app/page.tsx into a
new AuthProvider at src/contexts/AuthContext.tsx. Wrapped at the root layout
so login/onboarding/dashboard routes all have access via useAuth().

Day 1 foundation for the App Router migration: migrated (dashboard)/X/page.tsx
route entry points won't have a parent passing props, so shared auth state
must live in a context they can read from.

Sub-components are unchanged — they still receive accessToken/userID/userRole
as props from page.tsx (which now reads them from useAuth()). Only the
page.tsx → top-level-page-component handoff is de-drilled; deeper prop
drilling is left for the per-page migration to address.

Net change: -86 lines from page.tsx (state + two effects moved), +5 in
layout.tsx (provider wrap), new AuthContext.tsx (~140 lines), test update
to wrap CreateKeyPage in AuthProvider.

Fixes LIT-3366
Part of LIT-3128

* fix(ui): await getUiConfig before clearing authLoading

The AuthContext refactor flipped authLoading to false synchronously on mount
while letting getUiConfig() run fire-and-forget. On SERVER_ROOT_PATH deployments
this races the unauthenticated login-redirect effect: the redirect fires with
proxyBaseUrl still at its module-init value, sending users to /ui/login instead
of {SERVER_ROOT_PATH}/ui/login.

Restores the original sequencing inside AuthProvider's mount effect and adds a
Playwright spec wired into the existing SERVER_ROOT_PATH workflow matrix. The
spec delays the config endpoint via page.route() to make the race deterministic
across CI runners.

.github/workflows/test_server_root_path.yml

@@ -101,6 +101,31 @@ jobs:
           docker logs litellm-test
           exit 1
 
+      - name: Setup Node for Playwright
+        uses: actions/setup-node@49933ea5288caeca8642d1e84afbd3f7d6820020 # v4.4.0
+        with:
+          node-version: "20"
+
+      - name: Install UI deps and Chromium
+        working-directory: ui/litellm-dashboard
+        run: |
+          npm ci
+          npx playwright install --with-deps chromium
+
+      - name: Run SERVER_ROOT_PATH redirect e2e
+        working-directory: ui/litellm-dashboard
+        env:
+          SERVER_ROOT_PATH: ${{ matrix.root_path }}
+        run: npx playwright test --config=e2e_tests/serverRootPath.config.ts
+
+      - name: Upload Playwright artifacts on failure
+        if: failure()
+        uses: actions/upload-artifact@ea165f8d65b6e75b540449e92b4886f43607fa02 # v4.6.2
+        with:
+          name: playwright-trace-${{ strategy.job-index }}
+          path: ui/litellm-dashboard/test-results/
+          retention-days: 7
+
       - name: Cleanup
         if: always()
         run: |