fix(research): expose manage_research as a native tool

[asd-standard]

Summary

manage_research (list/read/delete saved deep-research reports) was fully implemented and indexed but missing from FUNCTION_TOOL_SCHEMAS, so native function-calling models reported it as unavailable. This registers the native schema (action list/read/delete, id, search) and makes the generic "research" keyword hint co-select it alongside trigger_research, matching the sibling manage_documents tool.

Target branch

• This PR targets dev, not main. All PRs land in dev.

Linked Issue

Fixes #2130

Type of Change

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

Checklist

• I searched open issues and open PRs — this is not a duplicate. (manage_research tool is invisible to native function-calling models #2130 is open; prior PRs fix: manage_research tool is invisible to native function-calling models #1877/[codex] fix(tools): expose manage_research schema #2313 were self-closed without merging; this supersedes them and targets dev.)
• 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 and verified the change works end-to-end: on a native/API model, "list my research" / "read my research reports" now surfaces manage_research and returns the saved report.

How to Test

1. Run the app (Docker or uvicorn).
2. On a native function-calling (API) model, ask "list my research" or "read my research reports".
3. Confirm manage_research appears in the tool list and returns the report text + sources. Before this fix, the model reported it had no manage_research tool.
4. python -m pytest tests/test_manage_research_tool_schema.py tests/test_tool_index_schema_parity.py tests/test_tool_rag_keyword_hints.py -q
5. python -m py_compile src/tool_schemas.py src/tool_index.py

Visual / UI changes — REQUIRED if you touched anything that renders

No visual/UI change — Python-only (src/), no static/, CSS, or HTML files modified.

Screenshots / clips

Not applicable.

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Transparency: this PR was AI-assisted (DeepSeek-v4-pro). It is a single, targeted, issue-backed fix, not a bulk auto-generated PR. Commits carry a Co-Authored-By: DeepSeek-v4-pro trailer.