The hippocampus does NOTHING.
It is the appendix of the brain. https://advances.sciencemag.org/content/6/29/eaaz0484

"If the hippocampus is critical for [transitive inference] & the formation of ordered representations, selective hippocampal lesions should impair monkeys’ ability to infer the relation of the nonadjacent pairs and should abolish the [symbolic distance effect]."

THEY DIDN'T

" If the primate hippocampus is critical for remembering temporal order, monkeys with selective hippocampal damage should be impaired in overall accuracy and the [symbolic distance effect] should be attenuated."

THEY WEREN'T

"The literature suggests that hippocampal damage will reduce accuracy & disrupt the SDE when monkeys are required to flexibly report the order of nonadjacent items, and that this impairment will be greater for between-list pairs than within-list pairs."

IT DID NOT

"...HPC damage should cause a shift to a recognition strategy that relies on a vague familiarity signal...monkeys with HPC damage would show a change in the pattern of false alarms made during normal & speeded recognition and to recently seen lures.

THERE WAS NO CHANGE

"If the HPC is selectively necessary for source memory but not item memory, then monkeys w/ selective HPC damage should still be able to discriminate between studied & unstudied items but should be impaired at discriminating between the two types of studied items."

THEY WERE NOT

"We hope to draw attention to the fact that applying findings from rodents—or monkeys—to humans requires nuance and comes with a host of caveats that are too often left unstated."

"Because results from different species present different advantages and limitations, a robust theory of HPC function must rest on a confluence of evidence from multiple species."

Here's a related hot take from David Gaffan on "not-hippocampus" from more than 20 years ago

https://pubmed.ncbi.nlm.nih.gov/21223918/