Hi @SvenGlöckner ,
From my understanding, you can't directly add your LogicApp to the Git through azure portal in Consumption Plan. You have to download the ARMTemplate (Azure Resource Manager templates) from portal, add it to the Git and then deploy the LogicApp to different environments through script. If you need to modify the LogicApp, you can clone the existing one and made the required modifications on the cloned one, then get the changes from the Export template
option and add it to the ARMTemplate you have in Git.
Although there is a Version
option in the LogicApp (not related to Git), where you can see the different Code Versions. Please see the screenshot below. Hope this will help. Thanks!