Which switch with POE and 16 or 24 ports

May I ask right away about this topic, which cables you are installing / pulling? Cat 5 or Cat 6 or already Cat 7 in the single-family house?

Cat 7, everything else (both upwards and downwards) currently doesn't make much sense.

already Cat 7

Why already? That was completely normal 10 years ago.

Yes, Cat 7 is simply more future-proof. Because I think the current standard family simply wouldn't need the speeds that Cat 7 offers. And it's simply three times as expensive as Cat 5. But as I said, to be future-proof, Cat 7 is probably the current standard.

Of course I could dismantle all this, but time is pressing on me.

What do you mean by saying time is pressing on you?

You could also take the approach of first buying the cheapest device on Amazon to activate the ports you really need urgently. TP-Link TL-SG1005P 5-Port Gigabit PoE Switch - 40€ Or simply connect all the ports of the FritzBox.

And then when you have time, you properly redo everything with a 19" rack etc.

And it is simply 3 times as expensive as Cat 5.

How many kilometers do you plan to lay? We're talking about differences in the range of two- to at most just under three-digit amounts in a normal single-family house.