[Core] Remove legacy stage config exports

[maithilijoshi20]

Summary

• remove the legacy StageConfig and merge_pipeline_deploy names from the public vllm_omni.config surface
• point the configuration API docs at VllmOmniConfig
• add a regression test that keeps the legacy bridge names out of __all__ and module attributes

This is the public API migration slice of #6500 and follows the structured runtime startup work merged in #6849. The legacy implementation remains available from its owning internal module for compatibility-only callers; this PR removes only the top-level public exports.

Validation

• ruff format --check tests/config/test_config_import_cycle.py
• ruff check tests/config/test_config_import_cycle.py vllm_omni/config/__init__.py
• python -m py_compile vllm_omni/config/__init__.py tests/config/test_config_import_cycle.py
• git diff --check
• tests/config/test_config_import_cycle.py : 6 passed

[vllm-omni-review-bot]

This PR appears to belong to: docs/design/module/vllm_omni_config.md, docs/design/module/entrypoints.md, docs/design/module/stage_runtime.md.

Module owners: @lishunyang12 @alex-jw-brooks @fake0fan

Routing: @lishunyang12 via module of the changed files, module named in the PR description, semantic router, CODEOWNERS; @alex-jw-brooks via module of the changed files, module named in the PR description, semantic router; @fake0fan via module of the changed files

@maithilijoshi20, please review your own changes and leave a short self-review comment describing what you checked. PRs without author self-review may not be assigned a reviewer.

Please take a look when you have a chance. If you would like an automated review, mention @vllm-omni-review-bot in a comment.

[vllm-omni-review-bot]

Omni ReviewBot triage note

Automated triage of commit bf056cfecab8 produced:

• Priority: high. Prompt maintainer attention is suggested.

These are automated triage suggestions only — the final decision belongs to the maintainers.

[NickCao]

This is covered in #8077