[LinuxBender]

This may be too complex of a setup but if that were my task I would install one of the open source NVM's like ZoneMinder [1][2], get a few cameras and use port forwarding to HAProxy with basic authentication to keep bots off the ZoneMinder interface in the event of vulnerabilities. This is only useful if you are not behind CG-NAT otherwise a VPN would have to be established from the home to a VM somewhere and then use that VM as the entry-point. Your extended family members could also have a browser open watching what is going on in your home.

That ZoneMinder or other open source NVM would double as home security so you could also watch all the doors, windows, yards, driveway, garage, etc... Each NVM will have a webpage that lists the compatible cameras.

I assume you mean to watch the baby while a babysitter is there and the baby is not truly alone. There are also some NannyCam devices that hide the camera so you can also keep an eye on what the babysitter is doing with the baby in multiple rooms.

None of this addresses E2EE but the server would be hosted in your house and would be using TLS to your web browser to watch it.

[1] - https://zoneminder.com/

[2] - https://www.youtube.com/watch?v=Us20t1gQPOE