yet we know from our own experience that there is something there [an experiencer] which does not want to be killed or suffer injury.
Think on those definitions for a moment, though.
What is "killed" or "injured"? To what molecular cell structure?
The basic reaction that we observe on the cellular level is akin to a desire for boundary, containment, and solidarity within its unit.
Cells typically only appear to break this conservation if there is potential of gain in some nutrient in the exchange.
Cells work like Bronze Age city-states, essentially.
A wall surrounding, a network of exchanges and conversions within that produce the gain of nutrients cyclically between components within, and the transfer between it and other cells should the right product arrive without threat to the integrity of the "cell-city-state".
If anything, I would flip your quandary around and state that humanity reflects our smallest biological components rather than examining how our smallest components have what appears to be a concept we have at high levels of cognition.
Take, for example, globalization: what happens in a dish with multiple cultures of bacteria?
At first? Nothing. They all develop rather independent of each other.
Then little by little they near each other from growth.
Then they begin touching, possibly moving away where needed, or attempting to combine in part.
Eventually, space is removed as a liberty and all cultures of bacteria are forced to an ultimatum of lacking space for continued growth mostly independently.
Either they all die, all but one dies and it is the successor, some die and some combine into a new culture that survives, or they all combine into one "globalized" culture.
The question, then, is regarding when looking at a cell; is it regarding death?
Or, possibly, instead is it regarding retention and not death?
Instead of "knowing" anything, the cell is running on a program of instructions that are saved and permeated into it (rna, dna, protein) which determine the type of reaction to have to alterations to its components.
This then, brings your question down to the subject of why dna has storage capacity at all.
But this is empty, because truly, it actually leads down to the simpler form: rna.
So the question becomes primarily: how does rna work, how did it come to be this way, and why?