I think perhaps you are coming at this from the wrong angle.. git push is your backup (assuming you are using an offsite git server/service) - and should also be the trigger for automation in CI - ie you push your git commits, the CI server detects those changes and fires off a build, runs your unit tests, builds your installer, ftp's the files to the server and sends out email notificiations.
(vendor plug)
These days CI is very accessible even for solo developers. Our Continua CI product is free for a single concurrent build and a single build agent (installed on the same machine as the server) - other than that it's fully functional, unlimited configurations (and users) - perfect for solo developers and it's very easy to scale it up (add licenses, install extra agents as needed). It only takes a few minute to install and get up and running with a build process -
The video shows using mercurial, visual studio and nunit, but it works just as well using git, delphi and dunitx.
https://www.finalbuilder.com/resources/blogs/building-delphi-projects-with-continua-ci
If you really want to expand your automation then take a look at FinalBuilder (built with delphi) - over 600 built in actions that cover version control (git, mercurial, svn and a bunch of others), compilation (delphi 3 - 11, msbuild, vs etc) - install builders (innosetup, installshield etc), deployment (FTP/FPTS/SFTP/SSH) and a too many others to mention here.
The cool thing about FinalBuilder is you get to develop and debug your build process in an IDE that lets you step through your build process, stop on breakpoints, watch variables etc.. and then your build project can be checked into version control along with your source code and your CI server can run FinalBuilder to build your projects (using the console version of FinalBuilder).
Of course Continua CI and FinalBuilder play very nicely together - we build FinalBuilder, Automise and Continua CI with FinalBuilder an Continua CI.
https://www.finalbuilder.com/resources/blogs/continuous-integration-with-finalbuilder