Prevent Stale Release Plans Caused by Unmerged Approved SDK Pull Requests

**Problem Statement**
A release plan can enter an inconsistent state when SDK pull requests are merged and released for only a subset of supported languages.

The first SDK pull request merged under a release plan is typically a strong signal that the service is ready for SDK release. However, service teams may occasionally overlook remaining language-specific SDK pull requests, leaving them approved but unmerged. As a result:

Only some language SDKs are released.
Remaining language SDK pull requests become stale and idle.
Release plans remain incomplete for extended periods.
Customers experience inconsistent SDK availability across languages.

**Proposed Solution**

Identify release plans where:

- At least one SDK pull request has been merged.
- One or more SDK pull requests for other languages remain open.
- The remaining pull requests satisfy auto-merge requirements (approved and passing required validations).

Action:

When the first SDK pull request is merged under a release plan:

1. Detect all remaining eligible language SDK pull requests associated with the same release plan.
2. Automatically apply the `auto-merge` label to those pull requests.
3. Allow the existing auto-merge workflow to merge the remaining SDK pull requests.

**Benefits**

- Prevents partial SDK releases across languages.
- Reduces stale SDK pull requests.
- Improves release plan completion rates.
- Ensures a consistent release experience across all supported languages.
- Eliminates manual follow-up for forgotten language SDK pull requests.

**Summary**

Once a service begins releasing SDKs for a release plan, the system should assume that all remaining approved and validated language SDK pull requests are intended for release and automatically move them toward completion.

Start by locating the release-plan handling and the existing auto-merge workflow described in the issue. Trace how merged SDK pull requests and approval or validation status are detected, then verify that eligible pull requests for remaining languages receive the auto-merge label and complete the release plan consistently.

Written by the indexing model from the issue text.