revert: "chore: remove _experimental/out" (#31546)

[yuneng-berri]

Relevant issues

Reverts #31546

Linear ticket

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Screenshots / Proof of Fix

With the export restored, a proxy started from a plain git checkout serves the bundled admin UI again without running the dashboard build first:

$ curl -sS -o /dev/null -w 'GET /ui/ -> %{http_code} %{content_type} %{size_download} bytes\n' http://localhost:4001/ui/
GET /ui/ -> 200 text/html; charset=utf-8 22340 bytes

$ curl -sS -o /dev/null -w 'GET /get_image -> %{http_code} %{content_type}\n' http://localhost:4001/get_image
GET /get_image -> 200 image/jpeg

tests/test_litellm/proxy/test_proxy_server.py (which this revert also restores to its pre-#31546 state) passes: 214 passed

Type

🧹 Refactoring

Changes

Clean git revert of the #31546 squash commit (72bcb74), no conflicts. It restores the committed admin UI export under litellm/proxy/_experimental/out/ and rolls back the changes that made the codebase tolerate its absence: the get_favicon swagger fallback, the check_dir=False static mounts, the module-level _restructure_ui_html_files, the mkdir -p in the UI build scripts, the .gitignore entry, and the synthetic-export rewrite of test_admin_ui_export_serves_nested_extensionless_routes

Four commits landed on litellm_internal_staging after #31546 that touch proxy_server.py (#31775, #31754, #31753, #31578); they are in unrelated areas (MCP registry hydration, audit logging, spend counters) and the revert applied without touching their hunks

[greptile-apps]

Too many files changed for review. (709 files found, 100 file limit)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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