It's a shame because there *has* been a lot of deep work done on what kind of computer life is. People often use the Chomsky Hierarchy (https://en.wikipedia.org/wiki/Chomsky_hierarchy) to define the different types of computer vs automata. Importantly, a classical Turing machine is Type-0 on the Chomsky Hierarchy. Depending on what parts you include from a biological system, you could argue it's anywhere from Type-0 to Type-4.
Interestingly, the PhD thesis of well-known geneticist Aviv Regev was to show that certain combinations of enzymes with chemical concentration states are enough to emulate pi-calculus, and therefore are Turing machines! https://psb.stanford.edu/psb-online/proceedings/psb01/regev....