fix(research): expose resolved model in API and logs (#4567)

[Elshayib]

Summary

Include model in /api/research/start and status payloads and log when admin research overrides differ from the session model.

Target branch

• This PR targets dev, not main. All PRs land in dev; main is curated by the maintainer at each release. If your PR is on main by accident, click "Edit" on this PR and change the base.

Linked Issue

Fixes #4567

Type of Change

• Bug fix (non-breaking — fixes a confirmed issue)

Checklist

• I searched open issues and open PRs — this is not a duplicate.
• This PR targets dev
• My changes are limited to the scope described above — no unrelated refactors or whitespace changes mixed in.
• Verified with targeted pytest / syntax checks.

How to Test

1. Configure a research-specific model override. 2. Start deep research. 3. Start response and status JSON include model field; server log notes override.