LAN and Wi-Fi "devices" per floor?

But it actually doesn't make any sense. Because if I want to use such a socket, I first have to run down to the basement and patch the connection.

The photos may not be from private houses, but from administrative or commercial buildings. It often makes sense here to terminate all connection sockets at the patch panel (at the back), and then, if necessary, connect the respective socket to the switch (and thus to the LAN) - or not. This way, it can be prevented that someone quickly plugs into the network in an empty office or a public space. And if the need arises, it is much more comfortable to plug the patch cable in the server room than to fiddle around with the floor socket.

But why do photos of patch panels show, for example, 16 patched LAN cables plugged in at the back, but only, for example, 5 LAN cables in the switch ports?

In your example, apparently only five of sixteen potential endpoints are actually used, i.e. only five of the sixteen sockets have users.

Assuming I have a 24-port patch panel, then I wouldn't need a 24-port switch, right?

The number of ports on the patch panel is always greater than or equal to those on the switches in general, and certainly greater than the PoE-powered switch ports. If an office has four corners but only three desks, only three workers use their computers, but the fourth corner is also wired, and this cabling at the server room end is not just thrown somewhere. Therefore, temporarily unused ports on the panel are the rule. A switch is an electronic "Fräulein vom Amt" and serves all available workplaces - so none are held in reserve. And injectors for PoE are sometimes only available on part of a switch’s ports because not every endpoint requires PoE. Power over Ethernet (meaning the modulation of power supply for device operation onto the line used for data exchange) is mainly needed where, in an office telephone system, a separate power adapter cable should not be used for every IP phone. The plug-in power supplies are comparably cheap s**t and are also often avoided fire hazards.

The patch panel is nothing other than the orderly collection of cable ends.

A plug-terminated orderly collection, to be more precise.

This can prevent someone from quickly plugging into the network in an empty office or public space.

The system administrator prevents this through permissions, which are by no means related to the use of the sockets.

You can also use network cables for other applications, e.g. HDMI to LAN and then back to HDMI (even with HD Audio) or USB over LAN (I used that before) or patch the incoming phone socket to where you want to have the router. In that case, it's also bad if you generally connect all incoming cables to the switch. In my case, I would have needed 2x48 port switches.

One can also use network cables for other applications, e.g. HDMI over LAN and then back to HDMI (even with HD audio) or USB over LAN (I used that before) or patch the incoming telephone socket to where you want to have the router. In that case, it is also stupid if you generally connect all incoming cables to the switch.

Yes exactly, a patch panel is absolutely passive and therefore on the other hand completely protocol-neutral, whereas a switch of course can only serve those components through its ports that basically operate in the same world.