So say suppose you're in New Orleans and I am in San Jose, now we can compare our distance, because geographical distance usually equates to cultural differences and perceptions of quality.
For a decade and a half, Yandex has had a codename for each big revision of search ranking algorithms and release of new search features. Most were city names, and Magadan was one of them. So “distance” is probably a distance to some rating introduced in that release. Whether it is a positive or negative factor (cutting obvious over-optimized sites), I have no idea.
In other words, clickbait images from clickbait ad networks.
I don't know if either of these are relevant here, but it's possible a weight on Yellow Images could be related to NSFW images.
So my suspicion above is probably wrong, and "yellow" images probably refer to a Toloka score/color for whatever domain the images are hosted on.
[0] https://yandex-explorer.herokuapp.com/search?q=yellow&o=all
Was the agencies.json published?
I agree though, would be very interesting indeed to see who they promote and/or push down
108 MusicQ: The musicality of the request. The results of the sorcerer Anton Konygin.
276 NightQuery: The request is set mainly at night (and accompanying ones for morning, afternoon etc)
316 IsUa: Domain in the .ua zone (ukraine)
747 WordHostWikiSum: The relative popularity of the Word -Host pair, where Word is the word from the Title article on Wikipedia, and the Host is the host that is referred to in this article.
755 NastyContent: Content ugliness factor. (several of the other factors related to port and "adult" content are defined as multiples of this)
892 ShortVideo: A document is a short video (Tiktok, Reels, Shorts)
894 TelegramPost: Document - post in telegram (note I could not find similar for twitter etc, but they do have for tiktok)
1076 More90SecVisitsShare: The share of visits for which the time spent during the day on the host is more than 90 seconds (they track how long users are spending on pages)
1078 RankHackedNovaPhp: Rank of hacked sites
1309 DistanceToAnkara: The distance from the city from where the request was set to Ankara
1603 YellowImgCount: Average yellow images count on host
1614 NewsAgencyRating: Rating of news agency from agencies.json (Yandex.News resource)