There is currently no supported API for extracting hidden subtitle tracks for arbitrary videos. (You may be able to reconstruct some methods of obtaining this data, but this is not supported, and I cannot encourage it.)
The officially supported header methods for the v2 YouTube Data API are documented at https://developers.google.com/youtube/2.0/developers_guide_protocol_captions
Only an authenticated request that owns this video will display a list of subtitle tracks and allow you to download them in .srt or .sub format (not JSON).
I would expect that at some point there will be methods for interacting with headers in the v3 API, but unfortunately I do not have any specific information to share what might happen.
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