feat: LM Studio Integration (#53248)

* Feat: LM Studio Integration

* Format

* Support usage in streaming true

Fix token count

* Add custom window check

* Drop max tokens fallback

* tweak docs

Update generated

* Avoid error if stale header does not resolve

* Fix test

* Fix test

* Fix rebase issues

Trim code

* Fix tests

Drop keyless

Fixes

* Fix linter issues in tests

* Update generated artifacts

* Do not have fatal header resoltuion for discovery

* Do the same for API key as well

* fix: honor lmstudio preload runtime auth

* fix: clear stale lmstudio header auth

* fix: lazy-load lmstudio runtime facade

* fix: preserve lmstudio shared synthetic auth

* fix: clear stale lmstudio header auth in discovery

* fix: prefer lmstudio header auth for discovery

* fix: honor lmstudio header auth in warmup paths

* fix: clear stale lmstudio profile auth

* fix: ignore lmstudio env auth on header migration

* fix: use local lmstudio setup seam

* fix: resolve lmstudio rebase fallout

---------

Co-authored-by: Frank Yang <frank.ekn@gmail.com>

.github/labeler.yml

@@ -293,6 +293,10 @@
   - changed-files:
       - any-glob-to-any-file:
           - "extensions/kilocode/**"
+"extensions: lmstudio":
+  - changed-files:
+      - any-glob-to-any-file:
+          - "extensions/lmstudio/**"
 "extensions: openai":
   - changed-files:
       - any-glob-to-any-file: