With the exception of New Age software like Go, that for some reason doesn't use manpages, I'm not convinced that the problem implied here actually exists.
If the goal is to find out which particular file is being used at this particular time, on this particular system, the maximum verbosity log might have that information, and otherwise strace can help, as described in the other comments.
The program already knows what config files it's loading and in what order, so why is it left up to the human to do all that work again? There should be a flag like --manifest or something that would spit out what actually got loaded from where.
Primarily because man pages need to go in the MANPATH to be useful but these tools tend to dwell somewhere in ~/.
So, following current practices, installing binaries in ~/.local/bin and man pages in ~/.local/share/man should work without any additional configuration.
> Ideally I'd like to avoid scanning all the way through the manual page or other documentation for the program to find out, because that's slow and annoying.