Introduce dependency_bump_web_search feature flag

What does this MR do and why?

Introduces the dependency_bump_web_search feature flag and pushes it to the AI Gateway via the Duo Workflow helpers (push_feature_flags), enabling web search capabilities for the dependency bump Duo flow. The flag is beta, default-disabled. Mirrors !219759 (merged).

References

• Feature flag issue: https://gitlab.com/gitlab-org/gitlab/-/work_items/604047
• Rollout issue: https://gitlab.com/gitlab-org/gitlab/-/work_items/605335
• Reference MR: !219759 (merged)

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