How do I reconnect my project to my existing GitHub repository

The easiest is to:

• clone your GitHub project
• cd in that local clone
• do a git --work-tree=/path/to/unzip/project diff to check if your zip has any differences with the version cloned from git hub: if it does, git add and commit. (and by that use git --work-tree=/path/to/unzip/project add -A . and then a simple git commit, to record the differences from the zip version of the project and the git cloned one)
• resume working with the local clone (which is a git repo)