Technically there are two clients: The camera and whatever device is used to access the feed.

I can absolutely imagine an architecture where video can be streamed in an encrypted manner, or stored in encrypted time-stamped blobs, allowing the server to provide rough searching, and then the client can perform fine-grained scanning.

This obviously doesn't enable any kind of processing of the video data on the server side, and doing it on the receiving client would require the feed to be active This means that any kind of processing would almost necessarily have to happen on the sending device, which would probably increase the power and compute requirements by a lot.