fix: resolve TypeScript errors with moduleResolution nodenext and skipLibCheck false

[R-Delfino95]

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 `/// ` 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

[vercel]

@R-Delfino95 is attempting to deploy a commit to the Mux Team on Vercel.

A member of the Team first needs to authorize it.

[snyk-io]

✅ Snyk checks have passed. No issues have been found so far.

Status	Scan Engine	Critical	High	Medium	Low	Total (0)
✅	Open Source Security	0	0	0	0	0 issues
✅	Licenses	0	0	0	0	0 issues

💻 Catch issues earlier using the plugins for VS Code, JetBrains IDEs, Visual Studio, and Eclipse.

[cursor]

Cursor Bugbot has reviewed your changes and found 1 potential issue.

^{❌ Bugbot Autofix is OFF. To automatically fix reported issues with cloud agents, enable autofix in the Cursor dashboard.}

^{Reviewed by Cursor Bugbot for commit 289670b. Configure here.}