[codex] Fix FastMCP context argument schemas

[cobanov]

Summary

Fix FastMCP tool registration so internal Context parameters are injected by the MCP server instead of being exposed as client-facing tool arguments.

Root Cause

The project uses from __future__ import annotations, so ctx: Context was stored as a postponed annotation string at runtime. FastMCP detects context parameters from the runtime annotation before building the tool input schema, so ctx was incorrectly included as a required MCP argument. Clients then failed tool calls with ctx Field required.

Changes

• Normalize ctx annotations to the runtime Context type before registering predefined tools, get_database_schema, and run_sql.
• Convert decorator-based registrations where needed so the annotation fix happens before FastMCP builds schemas.
• Add a regression test proving ctx is absent from client-facing tool schemas while run_sql still requires query.

Validation

• uv run ruff check src tests
• uv run pytest

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch codex/fix-fastmcp-context-schema

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