For inspiration I'll describe our setup:

We have a TP link TAPO camera, it sits on a VLAN without access to the internet. We can access and watch it through home assistant. There's a custom integration that allows for some control of the camera including motion control, motion and noise detection, though the basic integration should be fine by now for just the video and audio feed.

Since we have some notification set up when the motion or noise is triggered, we don't need to have the video feed open all the time (it even pops up on our Kodi TV). Though, we do use an old spare android phone as a dedicated baby monitor, but we're not tied to using just that one.

This is stationary for our home though and the initial setup of the camera does require internet connection, but after that... It all lives locally.

We also do have a cheap TrueLife video baby monitor, closed loop, with a dedicated receiver unit, but that is more of a travel solution. No fancy function, just video and audio feed from the camera to the parent unit. The range of this thing is rubbish though...
And when we don't need video feed, we use regular Motorola PMR walkie-talkies, one of them (on the child side) in VOX mode. Any baby monitor can only dream of its range and battery life...

So, that's our setup in a nutshell. If you'd like to know more, feel free to ask 😉