fix: resolve TypeScript errors with moduleResolution nodenext and skipLibCheck false (#1313)

Resolves #1299 

- Vendor \`mux-embed\`'s type declarations into
\`playback-core/src/vendor/mux-embed.ts\`. TypeScript compiles this into
\`dist/types/vendor/mux-embed.d.ts\` and emits a correct relative
reference path for consumers.
- Added a \`vendor:types\` npm script
(\`scripts/vendor-mux-embed-types.mjs\`) that copies the types directly
from \`node_modules/mux-embed/dist/types/mux-embed.d.ts\`. It's hooked
into \`prebuild:types\` so it runs automatically on every build, and a
separate \`verify:vendor\` script in CI fails the build if the committed
vendored copy drifts from the installed \`mux-embed\` — keeping the
source-of-truth honest at review time, not just at publish time.
- Moved \`@types/google_interactive_media_ads_types\` to
\`dependencies\` in \`mux-video\`.
- Removed the broken \`/// <reference path>\` from
\`mux-video/src/ads/index.ts\` — it's no longer needed since
playback-core's vendored reference propagates transitiv
- Stamp the resolved \`mux-embed\` version in the vendored file header
(\`// Source: mux-embed@X.Y.Z / ...\`) so type drift after a dependency
bump is visible at a glance in PR diffs.
- Validate that the package resolved in \`vendor-mux-embed-types.mjs\`
is actually \`mux-embed\` — defensive against edge cases in monorepo /
symlink layouts where the directory walk-up could resolve the wrong
\`package.json\`.

## Vendoring guardrails

To keep the vendored types honest over time:

| Guardrail | Where | What it catches |
|-----------|-------|-----------------|
| Version stamp in header | \`scripts/vendor-mux-embed-types.mjs\` |
Silent drift after a dependency bump |
| Package-name sanity check | \`scripts/vendor-mux-embed-types.mjs\` |
Wrong \`package.json\` resolved in non-standard layouts |
| \`verify:vendor\` in CI | \`scripts/verify-vendor-drift.mjs\` +
\`.github/workflows/ci.yml\` | Stale \`src/vendor/mux-embed.ts\`
committed without regeneration |

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Co-authored-by: Manuel Calleriza <mcalleriza@mux.com>
Co-authored-by: Claude Sonnet 4.6 <noreply@anthropic.com>