Connected MCP server tools are not always injected into Agent mode when tool-RAG filters schemas

[LeoYHTong]

Codex discovered a mismatch between the MCP integration UI and Agent-mode runtime tool availability.

## Summary

A user-added MCP server can appear connected in Settings, with all tools enabled, while Agent mode still cannot call those tools natively.

In this case:

- Settings showed the MCP server as connected.
- The MCP manager discovered the expected tools.
- The active Agent-mode chat did not receive the MCP tools as callable native function schemas.
- The model fell back to built-in tools instead.

## Root Cause

The issue appears to be in the Agent-mode tool selection path.

Connected MCP tools are converted into OpenAI-compatible function schemas named like:

```text
mcp__{server_id}__{tool_name}

However, when tool-RAG selects a relevant tool subset for the current turn, MCP schemas are included only if their exact dynamic names appear in the selected set.

If the tool index has not indexed those dynamic MCP tools, or the prompt does not retrieve them, the connected MCP tools are silently omitted from the model’s callable schema list.

So the UI connection state can be PASS while Agent-mode tool injection is FAIL.

Reproduction Pattern

1. Add a user MCP server through Settings → Integrations.
2. Confirm the integration shows connected and tools enabled.
3. Ask Agent mode to use one of those MCP tools.
4. The model may report only built-in tools and not see the MCP tools.

Minimal Fix

When the user prompt clearly indicates MCP/tool-server intent, include connected MCP schemas even if the normal tool-RAG relevant set does not contain their exact dynamic names.

Example patch shape:

_last_content = _last_user.lower()
_wants_mcp = any(kw in _last_content for kw in _MCP_KEYWORDS)

if _relevant_tools:
    base_schemas = [
        s for s in FUNCTION_TOOL_SCHEMAS
        if s.get("function", {}).get("name") in _relevant_tools
    ]

    if _wants_mcp:
        _mcp_filtered = mcp_schemas
    else:
        _mcp_filtered = [
            s for s in mcp_schemas
            if s.get("function", {}).get("name") in _relevant_tools
        ]

    all_tool_schemas = base_schemas + _mcp_filtered

Also consider expanding MCP intent keywords for common external data-source use cases, for example:

mcp
supabase
system_facts
report_index
open_cases
agent_registry
skills
query_system_facts
query_report_index
list_open_cases

Expected Behavior

If a user explicitly asks Agent mode to use MCP tools, connected MCP schemas should be included for that turn.

The Settings integration state and Agent-mode callable tool surface should not disagree silently.

<img width="658" height="525" alt="Screenshot 2026-06-07 at 9 22 54 PM" src="https://github.com/user-attachments/assets/1d24e60f-f64d-4418-8773-e0912f1cddeb" />