It's interesting to look at the primary literature, because then you realize how hard it is to sort these questions out and how many uncertainties there are, because there are a lot of different extinct lineages that might or might not have led to whales or hippos.

Here's the general group people seem to be fairly sure led to hippos; the ones that led to whales might have been an earlier group that gave rise to this group, or perhaps one of these, or perhaps not all whales share a 'root whale':

https://animals.fandom.com/wiki/Anthracotheriidae

The actual kind of data they use to make these judgements is mostly bone fragments from fossils, as comparing modern DNA of hippos and whales can only tell you so much. Here's an example study from 2003 on the hippo lineage:

https://wp.ufpel.edu.br/cdrehmer/files/2017/06/hipopotamo-ST...

I'd like to suggest OneZoom for exploring these relationships.

http://www.onezoom.org/life/@Hippopotamidae=510764?img=best_...

According to wiki it's the third last item in their list, Artiodactyls pakicetus:

https://en.m.wikipedia.org/wiki/Pakicetus

> the closest living non-cetacean relative being the hippopotamus.