Generally you would require some sort of compute that executes the automation, so that's why using a third party tool, even if it is Open Source might incur in a small additional cost. However, some of those have free tiers as well depending on the tool.
If all you need is pulling the code to Databricks, you can do it manually using Repos as mentioned in Option 1. However, any automation will require a server that runs the automation with any of the third party or Open Source tools - Jenkins, Github Actions, Terraform, etc.