Switch to new OpenAPI parser as default (#2513)

* Switch to new OpenAPI parser as default

Remove the legacy OpenAPI parser and make the experimental parser the
default. The experimental parser (introduced in 2.11) offers better
performance, improved compatibility, and a more maintainable architecture.

- Delete legacy parser (server/openapi.py, utilities/openapi.py)
- Move experimental parser to main locations
- Remove enable_new_openapi_parser feature flag
- Update documentation to remove experimental references

* Add deprecation stubs for experimental OpenAPI imports

* Add deprecated enable_new_openapi_parser setting and deprecation tests

* SDK docs

* REview comments

* Fix docstrings

* Update docstring

* Review comments

* Fix broken links

AGENTS.md

@@ -33,7 +33,7 @@ uv run pytest                        # Run full test suite
 | `├─prompts/`       | Prompt templates + `PromptManager`                  |
 | `├─cli/`           | FastMCP CLI commands (`run`, `dev`, `install`)      |
 | `├─contrib/`       | Community contributions (bulk caller, mixins)       |
-| `├─experimental/`  | Experimental features (new OpenAPI parser)          |
+| `├─experimental/`  | Experimental features (sampling handlers)           |
 | `└─utilities/`     | Shared utilities (logging, JSON schema, HTTP)       |
 | `tests/`           | Comprehensive pytest suite with markers             |
 | `docs/`            | Mintlify documentation (published to gofastmcp.com) |