But why should it be like something to convert short term memory to long term memory? Computational systems can convert data between different forms of memory but we don't typically believe consciousness emerges from this operation.
The alternative in this case is imagining that you have a biological process that has adaptive energy response controlling the movement from short term, to long term and itself optimizing based on the performance trade-off of input stimulus overload.
In that case, the process of deciding what to, and when to move data from short term to long term memory (in a feedback loop) could start to approach more of the appearance of consciousness (choosing what to process, what to remember, adjusting the input rate and types of input based on the limitations of processing and retention).
Many animals have consciousness as well so I think it's important to be more open to reducing the bare essentials of what a process of "awareness" is or could be rather than looking at it from a hyper evolved language/information influenced state of humans.
Note I agree that it is not consciousness, but i think it's an interesting exploration to look at the modeling of it from computer forms since we are made of non-conscious atoms and still made it here
Basically in this model, there is no present. The brain just invented the concept "I feel this" as a model of it's own inner workings, just like we invented the concept "object" to define certain aspects of physical reality that aren't 100% there.
So, basically you are imagining your experience, when in reality you are just an automaton. Same as how you imagine a robot is happy or sad when in reality it has no feelings.