Fix bug where attached docs were not part of the component documentation

[JReinhold]

This PR fixes an unfortunate regression, where MDX docs attached to components were not being output by the MCP server, even though they were present in the manifest.

[changeset-bot]

🦋 Changeset detected

Latest commit: bab8ec9

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 2 packages

Name	Type
@storybook/mcp	Patch
@storybook/addon-mcp	Patch

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[pkg-pr-new]

npm i https://pkg.pr.new/storybookjs/mcp/@storybook/addon-mcp@160

npm i https://pkg.pr.new/storybookjs/mcp/@storybook/mcp@160

commit: bab8ec9

[codecov]

❌ 1 Tests Failed:

Tests completed	Failed	Passed	Skipped
326	1	325	0

View the full list of 1 ❄️ flaky test(s)

apps/internal-storybook/tests/check-deps.e2e.test.ts > Storybook Dependencies > should be using latest versions from registry

Flake rate in main: 32.35% (Passed 23 times, Failed 11 times)

Stack Traces | 5.1s run time

Error: Storybook dependencies are outdated. Update the catalog in pnpm-workspace.yaml:

  sed -i '' 's/10\.3\.0-alpha\.4/10.3.0-alpha.6/g' pnpm-workspace.yaml && pnpm install

Outdated packages:
  - @storybook/addon-docs: 10.3.0-alpha.4 → 10.3.0-alpha.6
  - @storybook/react-vite: 10.3.0-alpha.4 → 10.3.0-alpha.6
  - storybook: 10.3.0-alpha.4 → 10.3.0-alpha.6
 ❯ tests/check-deps.e2e.test.ts:42:10

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[codecov]

Bundle Report

Changes will increase total bundle size by 40.13kB (100.0%) ⬆️⚠️, exceeding the configured threshold of 5%.

Bundle name	Size	Change
@storybook/mcp-esm	40.13kB	40.13kB (100%) ⬆️⚠️

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[kasperpeulen]

LGTM