Satellite system recommendation

We have a simple meter cabinet. Next to it a sub-distributor for the heat pump. Above it hangs the fiber optic modem. On the meter cabinet sits the Fritzbox. Next to it a switch (simple TP-LINK). Above that the electrician has laid the Homeway cabling.
I don't know if I can or want to cram all of this into one network cabinet. But if the multiswitch is added and later my microserver, I don't know if that will still look "good."

Everything I've seen so far are rather "deep" cabinets but I want it to be more shallow (similar to the meter cabinet) also because I want to bolt it to the wall.

Make sure to take a detailed photo of the patch panel where the network cables are terminated. If things go badly, a small "operation" might be necessary to get the cables into the network cabinet at all.

If I understood you correctly, you are looking for something like a Hager multimedia distributor. I can't say if everything fits in there as you want it.

I would save myself a box and just nail everything neatly organized to the wall without a cabinet. If the patch panel is mounted as shown in the pictures with the ports facing upwards, then it should be directly rotated. Either ports to the side or better downwards. The reason is that dirt and similar things remain inside if ports face upwards. Where is the grounding of the patch panel? Do I just not see it or is there none?