Can Youtube Data API v3 provide a list that matches the suggested videos that pop up when a video finishes playing?

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Can Youtube Data API v3 provide a list that matches the suggested videos that pop up when a video finishes playing?
Original Question
Like this asker, I want to get the list of suggestions found on the right side of youtube.com/watch page. The first twelve of these pop up when a video finishes playing. By clicking "Show More" at the end of the list, an additional 30 or so videos are revealed.
I can get a list of loosely related videos by using YouTube Data API v3 search:list relatedToVideoId as suggested in this question.
Unfortunately, the list returned by search:list:relatedToVideoId is not the same as youtube.com/watch suggestions. Qualitatively, the list returned by search:list:relatedToVideoId seems to offer a wider variety of videos, many of which I haven't watched before, whereas the videos suggested on youtube.com/watch are mostly videos I have watched before, though they may be less closely related to the current video. The youtube.com/watch videos may be a subset of the total search:list:relatedToVideoId results, but I don't think so. Like this asker, I am interested in the youtube.com/watch list.
I can get the youtube.com/watch suggested videos manually by exploring the iframe document in Developers Tools and searching for elements with class="ytp-suggestion-set", but I can't access the iframe document in my javascript code due to Same-origin Policy.
class="ytp-suggestion-set"
Others have asked about the differences between the YouTube Data API results and results obtained from youtube.com, such as this question about search strings. In this answer, the responder says:
if you are logged in in youtube, youtube will order the results taking in account videos you watched or liked, while the data api does not have access to this info.
Edit
GET https://www.googleapis.com/youtube/v3/search?part=snippet&maxResults=50&relatedToVideoId=BcCaQhkAVIY&type=video&key=YOUR_API_KEY
GET https://www.googleapis.com/youtube/v3/search?part=snippet&maxResults=50&relatedToVideoId=BcCaQhkAVIY&type=video&key=YOUR_API_KEY
Using the google api explorer, I tried the request shown above twice with and without OAuth and got identical results. I am taking this to mean that the quote above applies to my case as well: search:list:relatedToVideoId does not take into account videos I have watched or liked.
At this time, I have found no way to get the "Up Next" or other suggested videos to use in my web app.
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