Google doesn't necessarily have to do anything special for YouTube, though. Google could "just" index YouTube videos as if they were any other web pages, in a standard way. It would then be YouTube's job, to make the data inside those video pages legible to Google's indexer. Where Google could enable this, by pushing for web standards to increase machine-legibility of video in HTML — e.g. standardized ARIA-accessible captions sources for the <video> element, etc.
If they got it set up such that in theory any web spider could come along and index a YouTube video — then there would be no anti-trust reason that Google couldn't just directly ingest the subtitle files off their own servers; it'd just be a bandwidth-saving optimization over the scraping process that they could otherwise do.
e.g. standardized ARIA-accessible captions sources for the <video> element, etc.
YouTube could literally be a minimal web forum with a video tag in the first post of each thread, but likely due to DRM and related motivations, they instead wrap everything in thick layers of obfuscated JS.
For a while there were various shady-looking sites that seemed to scrape YouTube video pages (including comments) and I could sometimes find them through Google (then going back to YouTube for the original video), but within the past few years those have unfortunately also either been delisted/censored from search results or died out.
If they got it set up such that in theory any web spider could come along and index a YouTube video — then there would be no anti-trust reason that Google couldn't just directly ingest the subtitle files off their own servers; it'd just be a bandwidth-saving optimization over the scraping process that they could otherwise do.