Security cameras, because our dog is a snorer...

In the evening, we sometimes just use our cameras to check things. Sometimes you can see that you have forgotten to put this or that away or something like that. Also to see who is standing at the door and ringing the bell, etc. The right word is a feeling of security. As already mentioned, cameras can also attract attention.

I am aware that there are qualitative differences in the cameras. But that is the case everywhere. How does it actually look legally? Am I allowed to film the entire entrance area? Or can the postman or someone similar complain? In times of the GDPR, everything has probably become a bit more sensitive?!

You are not allowed to monitor public areas. In addition, you must clearly mark it on your own property. See sign DSGVO video surveillance.

Rick has actually already counted up all the important things.
In addition to the investment costs of the cameras, there is also the storage medium, ideally a NAS, e.g. QNAP [haben wir in Kombination mit Hikvision Kameras] or Synology.
Furthermore (if you are serious about it), you have to think about an external backup, because what good is it if burglars break in and take or destroy your NAS.
We decided on the Magenta Cloud here, so we also save our data externally on Telekom servers.
This must happen practically in real time when the alarm is triggered, otherwise you have the problem regarding the theft of the NAS. NAS devices offer the so-called snapshot technology for this purpose.
On the topic of deterrence and cameras.
You need a proper concept, otherwise it is ineffective:

1) Fence
2) Perimeter surveillance (for those who don't care about money)
3) Cameras
4) Windows and doors
5) Intrusion detection system
6) Safe room (for those who really don't care about money anymore)

If the cameras report unauthorized access thanks to motion detection, action can be taken immediately, so cameras do make sense.

So if I monitor areas that are not accessed by the public (postman, Hermes courier, etc.), such as the garden area behind the house, the lawn area next to the house, garage driveway/carport driveway, do I not need a sign "Caution Video Surveillance"?

The path to the front door for the postman etc. would then remain unmonitored!

It should be enough if our little fighter-cuddler sits up on the gallery window ;-)

You are misunderstanding here publicly. Everything on your property is not public. You are allowed to monitor your driveway. The camera must only be set so that it does not film more than your property. This is basically possible with software in the camera. There have been a few rulings that this is not sufficient because it is not apparent from the outside. Then the camera must be equipped with a "privacy screen." No plaintiff, no judge. If you do not have a totally annoying neighbor, it does not really matter. People theoretically must also be informed about video surveillance in the garden. If you, for example, have only one entrance to the property, you put up a sign there. That way, you have fulfilled your obligation.