No, a Pi-Hole would not work in this case, as suggestions are not "ads", technically.
They probably did that by IP. Keep in mind that Google is an ad-company that makes money by profiling and Amazon wants you to buy their stuff. Of course Amazon gets info from Google to make more money out of you.
There might be a way to block Amazon recommendations, tho. Maybe even something officially supported, some kind of toggle in your profile config.
Also, don't use YouTube directly, use Invidious or Piped, and this particular issue would be gone.