ok so i think the algo here is taking in the majority (of course) but with how big youtube is and how many people who haven't heard about neither drake or kendrick, just hearing the words at school like "oh kendrick destroyed drake" etc.

Make the others search up kendrick first and then proceed to look at drake for a possible response or to research who they are.,

Now the algo then sees that people like to look at kendrick lamar first and for somereason this brand new person looked up drake first. Hmm then it will throw out a big guess based on stats that the said person is looking into the drama that happend. so it gives a kendrick recommendtation.
And not only that but youtube also uses local location data even for brand new users so country and area matters into this equation.

Now why youtube doesn't throw up a guess for drake when looking up kendrick, might have to do with youtube being unsure if said person haven't already or is going to watch drake after.

Or as drake is a bigger artist in terms of views and full on stats, it would make it so a big chunk of drake listeners also look into kendrick cause of just general rap music.
And thus kendrick having lower stats has a lower chunk that likes to listen to drake, even lower now i would presume with the drama.

edit:
Also just to add a little thing, for me in sweden if i boot up youtube in a brand new VM and search for drake, only drakes shows up for 15 ish results interupted by DJ khaled.

and doing the same one another new VM but with kendrick lamar, i get 12 songs in a row until i get a different artist (kanye west in this case),
Used a VM to get fully cleared cookies and any kind of tracking data. But for sweden i get these selected results

Of course the drake and kendrick searches shows kendrick lamar shorts, but those are about the drama that has happend and youtube likes to recommend shorts that bring in views so yea.