ref(mcp): Use mcp_types package

[alexander-alderman-webb]

Description

According to the release notes:

Protocol types are a standalone package. mcp-types (imported as mcp_types) depends only on pydantic and typing-extensions, so tooling can speak MCP without the transport stack. Published in lock-step with mcp.

Issues

Reminders

• Please add tests to validate your changes, and lint your code using uv run ruff.
• Add GH Issue ID & Linear ID (if applicable)
• PR title should use conventional commit style (feat:, fix:, ref:, meta:)
• For external contributors: CONTRIBUTING.md, Sentry SDK development docs, Discord community

[github-actions]

Codecov Results 📊

✅ 90302 passed | ⏭️ 6310 skipped | Total: 96612 | Pass Rate: 93.47% | Execution Time: 320m 18s

📊 Comparison with Base Branch

Metric	Change
Total Tests	📈 +265
Passed Tests	📈 +257
Failed Tests	—
Skipped Tests	📈 +8

All tests are passing successfully.

✅ Patch coverage is 100.00%. Project has 2414 uncovered lines.
✅ Project coverage is 89.9%. Comparing base (base) to head (head).

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
+ Coverage    89.74%    89.90%    +0.16%
==========================================
  Files          192       192         —
  Lines        23823     23898       +75
  Branches      8226      8242       +16
==========================================
+ Hits         21378     21484      +106
- Misses        2445      2414       -31
- Partials      1349      1345        -4

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