I think you nailed it. In my experience, the increase in complexity isn't necessarily inherent to the amount of code so much as the amount of abstraction used as code size increases.
I've worked on some large codebases that only used simple, well-understood and/or well-documented abstractions which didn't feel as nearly complex as other codebases with abstractions that were more complicated than they were worth.
The thing is not the total size but the boundaries and the understanding of each layer and how manageable each layer is for the humans modifying and mantaining it ... which is, of course, the total cognitive complexity.
X lines of simple code containing a bug vs X lines of complex code also containing a bug.
How long does it take for average joe coder to find it in both cases? Is the experiment really needed?
Of course, everything being equal, more code leads to more complexity.
In this context, complexity is related to human capacity to collectively read/understand/maintain a code base.
I've been writing software almost non-stop for close to 25 years, and I still don't understand most of the code written by others.
I especially struggle to read anything with templates, generics, lambda...
But I can read straight C code, code written by Fabrice Bellard or John Carmack in the early days of id software.