If I include, say, a GPLv3 repository in in my repository using git subtree, would that count as distribution? Am I now required to license my repository as GPLv3 as well?
I don't intend to modify or interact with the GPL code, but I would like to have it in my repository for convenience and as a reference.
No, it does not. Distribution is when you provide the code to someone else. Simply moving code around within your own computer does not constitute distribution.
When you downloaded this code (or cloned the public git repo), you are not the one distributing; whoever put that code up where you can download it is the distributor. As long as you stick to personal use, you are not distributing it and none of the GPL restrictions apply.
INAL, but I don't think it's even meaningful to talk about licensing a repository - at least not in the same way we talk about licensing code. A repository is just a container for managing code. Just like if you burn a GPL software on a CD, it does not make the entire CD GPL, forbidding you from burning proprietary software on it(though other things may forbid you from doing so). The same way with repositories - even if you put some GPL stuff in it, it doesn't force you to make the entire repository and everything in it GPL.
The only thing affected by the copyleft is other code - the actual application inside your repository - and how it is affected is determined by how it interacts with the GPL software.
If that repository is public, yes, you obviously published it.
Otherwise obviously not.
And if you publish something, you better have the right to do so.
While you can have gpl and non-gpl code side-by-side in the same public repository, if one is the derived work of the other, remember that you must have the license to publish a derived work.
