fix(docs): correct v2 examples and make website builds deterministic

[OskarEichler]

Fixes

Use the v2 ref/method/getItemType APIs, remove the retired size estimate, and prepare layout animation before functional data updates. Stop website builds on failure, use the frozen JS lockfile and replace generated docs without nesting/stale pages. Repair malformed markup/Liquid filtering, label icon/video/iframe content and defer below-fold media loading.

Compatibility / observable changes

Website-only observable change: demonstration videos are user-started with controls instead of autoplaying. No runtime library API change. Build failures now stop publication preparation; no gem dependency or lockfile changes.

Verification

• Consumer verification: the combined fixes were packaged on the unchanged npm 2.3.2 runtime baseline and checked with React Native 0.87.1 / React 19.2.3. Immutable install, lint, both Android Debug variants, both unsigned iOS Simulator variants, four Metro bundles, 13 web targets and four browser-extension builds pass. All 298 installed non-metadata package files match the reviewed artifact byte-for-byte.
• Independent patch applied to 435b5141df4960ebbbc0b93264db3f5a4b23fffd: all 187 existing tests (14 suites), library TypeScript build and changed-file ESLint pass.
• One-off actual-source regression diagnostics pass:
  • website build stops after install failure
  • website build stops after docs failure
  • website build stops after jekyll failure
  • website build replaces docs without nesting
  • layout animation documentation uses the v2 ref API
  • current documentation only names the supported animation method
  • website snippet passes the item itself to getItemType
• The combined review workspace passes Android Debug, unsigned iOS Simulator Debug/Release, both production Metro bundles, web production export, Docusaurus/Jekyll builds and all 24 existing iOS Detox tests (10 suites). The contacts comparison was rerun after its final change. These combined-workspace results are not a claim that every device/platform was tested independently for this PR.
• No checked-in tests, reference screenshots, dependency versions or native SDK versions were changed.

Reviewers’ hat-rack 🎩

• Check the stated compatibility behavior and reproduce the relevant cases above.
• Run the existing test/type/lint commands and exercise the affected example or list behavior on your supported device matrix.

Physical-device behavior, Android Detox, assistive-technology conformance and release signing were not verified. No app deployment is part of this PR.

[OskarEichler]

I have signed the CLA!