fix(research): gate trigger_research behind the web-search toggle

[Ninthkitten]

Summary

With web search toggled off (the per-turn globe toggle in the chat input row), a research request still launched a full deep-research run. The toggle only disabled web_search/web_fetch — trigger_research was not counted as a web tool, so a model could reach the internet through the research path while the UI said web was off. This PR gates trigger_research with the same per-turn web toggle as the other web tools, everywhere that toggle opens or closes web access, so "web off" means offline.

Target branch

• This PR targets dev, not main.

Linked Issue

Fixes #5527

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.
• I actually ran the app (docker compose up) and verified the change works end-to-end. Type-checks and unit tests are not enough.

How to Test

1. Run the app, open a chat, and toggle web search OFF (globe icon in the chat input row).
2. Ask the model to research something ("do a deep research run on X").
3. Without this patch, a TRIGGER_RESEARCH run launches despite web being off.
4. With this patch, research is unavailable while the toggle is off; toggle web back ON and research works as before.

This fix has been running in a self-hosted deployment since 12 July and is verified in daily use.

🤖 Generated with Claude Code