Maybe a service that on event would proxy a stream from the camera and push a notification to your phone (or whatever you're using as a client).

On notification you could choose whether or not to record the stream and save it as a file on the client.

Said service could provide a guarantee that all data passing through its servers will not be recorded, persisted or even decrypted.

A Synology NAS with its built-in/free camera software, and cameras of your choice. Recordings live on the local NAS, you figure out how to get Synology's DS Cam app access to the local network. (I just use Synology's dynamic DNS service.)

What do you mean "without uploading the video somewhere" ?

If you are viewing it while not physically present it must be uploaded somewhere - otherwise it couldn't be on your phone right ?

MotionEye. Runs on anything from Raspberry Pis to regular computer. Handles multiple cameras, store locally/Dropbox/gdrive etc.