Which animal species has existed the longest?

A small nitpick. The title is misleading as it is not possible for a particular species to be identified as having lived the longest. The fossil record is very incomplete with soft parts missing. The distinctions between closely related species is often subjective depending on the differing views of taxonomists. Basically an academic discussion.
Not only that, but life has been re-cataloged with DNA, a completely new tree. So, without DNA, no one knows where to slot them in this new tree. A lot of changes were made when this was done. Not to mention the large number of new slots added, and the vast increase in present living life inventory.
Dec 14, 2022
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Crinoid fossils have been found to be over 430 million years old (Give or take a week)
They still exist today as Sea Lillys and even though they look like a plant they are actually an animal , an animal mind you that has survived 5 mass extinctions with very little change in looks or habbit due to evolution , Cephalopods also run the same age time however they have taken many evolutionary turns. The point being both of these species are older than the examples of youngsters they had here .... HuntingRocks YouTube I dig fossils
I believe that bacteria are the oldest living mobile organisms.
They were even preceded by non-mobile baceria (Bonnie Bassler).

Earth's earliest mobile organisms lived 2.1 billion years ago

Tubular structures found in black shale from a quarry in Gabon dating from 2.1 billion years ago - providing evidence of the earliest-known mobile organisms on Earth - are shown in Poitiers, France in this undated handout photo obtained February 11, 2019. Abderrazak Albani/IC2MP/CNRS/Universite de Poitiers/Handout via REUTERS