Looking for a bright outdoor lamp with an Ethernet camera for the house entrance

I do not recommend anything that is not really good...

If you have money to give away, want to be dependent on a cloud (a no-go in the security sector), and don't care about the appearance of the facade/entrance area, then you can take a look at Ring products. Otherwise, it's more something to satisfy the urge to play.

I won't even talk about the bitrate problems and other issues like audio dropouts (permanent)...

You are probably right, so I will really orient myself towards the following system:
- around the house good LED lamps with motion sensors
- an IP camera at the entrance area (I have now looked at the prices of the entry-level models of your three mentioned brands. It will probably be a Hikvision or Axis because Mobotix only starts at several hundred EUR. For example, something like the Hikvision DS-2CD2142FWD-I(2.8mm) IP Dome Camera came to my mind or which entry-level models would you recommend?)
- the IP camera connected through the facade via POE and an NVR on a NAS or other storage options inside the house
- next to the front door a simple doorbell intercom without camera because I want to cover the entrance area anyway with the IP camera
- a clearly visible alarm system dummy from ABUS?
Regards

Yes, that sounds like a concept. The Hiki you chose is okay for the beginning. I wouldn’t go below 4MP. You can gladly watch some videos to see what kind of images come out of it.

I had already dealt with the topic, as the child is growing and will eventually be home alone. However, I haven't made much progress.

Some cameras have the SD card inside the camera. Not practical, in my opinion.
Some cameras transmit the data somewhere in the cloud. Also not my case.
That leaves the IP camera solution proposed by Mycraft (I already have a NAS).
For pure surveillance or deterrence, that's clear, but how do I make the image (especially for the child) reasonably accessible when the doorbell rings (without KNX)?

Connecting a simple tablet somewhere in the hallway is one thing, but how do you make sure that as soon as the camera sends a signal, the tablet also turns on?
How do you plan this?

That is a very legitimate question and immediately points out to me the issue I forgot in my concept: the monitor in the entrance area inside the house. Yes, a simple tablet or LCD display and then control it via WLAN/LAN so that the NVR transmits it to the tablet through an app. But since, as I said, I have neither the time nor the money for KNX, it is really a very good question which app or hardware works for this without much effort?

The cameras always have an RTSP stream which can be displayed with VLC, for example, and whether to use the TV, tablet, or an extra display for playback is something you have to see. You can also manage something with the Raspberry. Or push notifications with an image when the doorbell is pressed. There are many possibilities.