I can't believe this is tiny module. It has almost everything related in file and directory. It doesn't have another dependency except core modules just as you expected. And documentation is very detailed and has many examples. There is no reason not to use this module at all.
As you know, LWP::UserAgent is powerful and enough to use and Net::Curl is really fast. But HTTP::Tiny is powerful and light-weight. Even you can do everything for HTTP with it, there is no more dependency except core modules. Since it is light weight and has no dependency, so this is best for your tiny script or little module.
If you want deal HTTPS then you will need non-core modules like IO::Socket::SSL and Net::SSLeay. So don't forget installing them. :)
Really awesome module if you want to write and use OO style perl module and script. I think there is no reason not to use this modue! I feel more comfortable with Moose rather than traditional C++ or Java's OO. If you already like and love moose, don't forget to check Moo either. :-)
This is really light-weight module. It does not support full featured of YAML, but it has no dependency with other modules, so it is really easy to embed your script or to use with App::FatPacker, etc... I usually embed this module into my script with App::FatPacker and support YAML features without other module dependency. ;-)
It's easy to use library without using command line git utility. Enough to fast due to libgit2 and really easy to use like other Perl module. I think document and example are needed but test code is good point to start. I really recommend this module if you have to handle git repository directly! :-)