Sorry for having to give you a negative response:

As far as I know, the answer to your question is no, there's no such API (and API endpoint for that matter) that will provide the URLs of the streams that YouTube does yield to its video players (embedded or not).

Of course, one may scrape this kind of info out of the YouTube's Web UI (like many tools available on the Internet do), but, if one does observe the DTOS specifications, will eventually come across the paragraph E.6 of section III. General Developer Policies, that explicitly forbids this activity.

An argument against the existence of such a API can also be derived from the DTOS document, same section III. General Developer Policies, but, in this case, from paragraph E.1:

E. Handling YouTube Data and Content

Aside from the permissions and rights granted in this section, you and your API Clients have no further permissions or rights to API Data, including to temporarily stored API Data.

1. Audiovisual Content

   You and your API Clients must not, and must not encourage, enable, or require others to:

   a. download, import, backup, cache, or store copies of YouTube audiovisual content without YouTube's prior written approval,
   b. make content available for offline playback
   c. [...]

Since is illegal to download video content from YouTube, it follows by simple formal logic, that it cannot exist an API that would provide URLs to the video content itself (under the assumption that the official APIs are formally consistent with the DTOS specifications).