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 📊

✅ 98741 passed | ⏭️ 6806 skipped | Total: 105547 | Pass Rate: 93.55% | Execution Time: 353m 38s

📊 Comparison with Base Branch

Metric	Change
Total Tests	—
Passed Tests	📈 +1
Failed Tests	📉 -1
Skipped Tests	—

➖ Removed Tests (1)

View removed tests

• test_circular_references_span_streaming
  • File: tests.tracing.test_misc

All tests are passing successfully.

✅ Patch coverage is 100.00%. Project has 2567 uncovered lines.
❌ Project coverage is 89.53%. Comparing base (base) to head (head).

Coverage diff

@@            Coverage Diff             @@
##          main       #PR       +/-##
==========================================
- Coverage    89.56%    89.53%    -0.03%
==========================================
  Files          193       193         —
  Lines        24520     24520         —
  Branches      8676      8676         —
==========================================
+ Hits         21960     21953        -7
- Misses        2560      2567        +7
- Partials      1400      1400         —

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