Is the fact that human emotional problems like depression and anxiety can seemingly reside in one brain hemisphere, but not the other, an example of a corresponding compartmentalization of cellular memory that actually houses the underlying trauma memories and distorted beliefs they caused?

You are putting two and two together here very nicely in having a greater awareness of the role of cellular memory, and thinking creatively as you review other phenomena you have witnessed over the years in the absence of an appreciation for cellular consciousness. The memory within various areas of the body, on a cellular level, can house trauma memories and bring about even severe symptoms without a concerted effort to resolve the wound that will exist perpetually until healing is obtained, because it is an energetic wound that extends to the akashic records and to the soul itself. That being the case, why would it not have an effect within the body as well? After all, that is not only where the problem begins, in the individual being part of something that ended tragically, with trauma unfolding to harm them, but it is also where the problem needs to be resolved and healing commence. If the person and their physical extension of the incarnation are not healed locally, the healing cannot spread further to change what is on record within the repository of life events among the akashic records, nor can the soul be repaired. So these phenomena are a clue not only to the workings of consciousness representing varied levels of the mind, the information is a vital clue about unmet healing needs and where to focus attention for the problem to be resolved in an effective fashion.