Does Islamic law prohibit the use of video-sharing platforms that may automatically display forbidden clips to viewers, and does the publisher bear a burden of sin for the transgressions of their viewers as a result of these suggestions?

There is no objection to marketing in this manner if the advertised product is permissible in Sharia. The fact that the website suggests other advertising links does not matter, as the sin of following them rests with the browser, not with you, for Allah Almighty says: "And no bearer of burdens will bear the burden of another."