Presumably if you had access to them you could fine tune them on your codebase.

Yeah, continuous online learning by fine-tuning seems like an obvious way of making these models recall information from outside the perceptible context. One could also prompt the model to (recursively) summarize code and prepend this summary to each prompt, and/or enable the model to interactively query function definitions or code summaries before outputting a final answer (trained by RLHF). But any such tricks might also quickly be outcompeted by an even more general model, e.g. one that directly controls the GUI and can communicate with coworkers...