This really depends on how the camera manufacture has set things up, but it will not go via the Google Assistant device (in this case the speaker).
Google Assistant Camera support works in much the same way as any other Chromecast video stream. This means that Google Assistant will send 2 URLs to the TV.
The first is to the viewer application. This is basically a HTML page that contains a video element it may be the generic Google provided one that is just a full screen video, or it may be a camera vendors customised version that may have their logo overlaid or similar.
The second URL is where to find the stream from the camera and here there are 2 options:
The camera natively supports one of the video formats that the Chromecast spec supports, in this case it could be a direct link to the camera.
The camera doesn't support any of the required video formats so the camera streams it's output to a cloud service run by the manufacturer where it can be transcoded and the link points to the cloud service.
Modern cameras tend to be capable of option 1 as this allows for the lowest latency and is more secure (since the video never leaves your home network). But having said that it means that the video feed is only available if the TV is on the same network. Option 2 means that you can also view the video stream when away from home, e.g. on your phone, which tends to be one of the key use cases for these sorts of camera.
Either way the video does not actually pass through your smart speaker (unless you are viewing the video on a Google Home Hub device with a screen).
The Google Home Local Control SDK is different and does not apply in this case.
