This is not as easy as it seems. The greenscreen+chroma filter just makes a "hole" into your video wherever green color is. Whatever source is behind the video, will shine through. In your case some picture. The video and OBS don't know anything about a camera moving. There is just a video with some transparent pixels and a source with an image that are overlaid on each other.
There is no functionality in OBS to get to track movement of any kind, and no functionality to move a source according to movement.
As far as I know, there is also not any plugin for this. This is functionality of really advanced and expensive movie production software.