Why would it be too narrow a topic? It's what you're writing about. It fits.
Emotions are tricky things. They are definitely NOT stimulus-response reactions--they are primarily learned behaviors and reactions. One thing I find most interesting in its falseness is the pervasive belief in simple dichotomies in life. This is one of them. Our emotions are complex things influenced by many, many things--chemicals, nerve impulses, memories, learned behaviors, our decisions, etc., etc., etc.
So, first I have some questions. Is a Sentient Digital Lifeform (which would require a different definition of 'lifeform' than the one I am familiar with) purely software, or does it include full integration a body/chassis which can influence its perceptions and input? Are there chemical reactions involved in its sentience, or purely software?
I think if it is pure software, then any 'emotions' would have to follow flowchart rules--basically, 'if this, then that.' It could be a very complex flowchart with multiple stimuli and processes going on simultaneously. But it would all have to follow logical processes. If chemical components & processes were thrown in, that could introduce a level of unpredictability, but otherwise, if the SDL is fully sentient of all its processes, any 'emotion' would have to be simulated at best.
However, I think that the emotions could be fairly 'real' if they included an important element: if the SDL's sentience did NOT cover all its processes. If its level of 'consciousness' and awareness only covered a limited amount of its processes, leaving certain behaviors and software or chemical outcomes confusing or not really understandable or knowable, it would be very real. I mean, that's mostly what we do, right? Maybe you are really exacting in keeping track of all receipts. You don't think about it, you may think it's what everyone does. But you do it because you grew up poor, and you have deep-seated fears of loss of financial independence or just poverty. You aren't thinking all that through, in fact you hardly notice it. But it affects your feelings and therefore your actions. There are complexities there, which if we could SEE all the processes and input and history, would make complete sense and seem transparent. But because so much is hidden or forgotten, and we don't see the process chain, it just seems 'emotional' and unpredictable.