It might not quite be there yet, but one key advantage large codebases have that I think LLMs in time will be able to better exploit is the detection of existing patterns - presuming they're consistent - and application to new code doing similar things or to fix bugs in existing code that deviates from the pattern in some way that causes a bug.
It's a different thing to what you're talking about, but it's one way I'd expect to see LLMs contribute a lot to productivity on larger codebases specifically.
large application codebase - consistent - have you worked in the field? I feel like usually there are 3 or 4 patterns from different people/teams at different points in time that spearheaded a particular ideology about how things "should" be done.
It's a different thing to what you're talking about, but it's one way I'd expect to see LLMs contribute a lot to productivity on larger codebases specifically.