That's a hard call. You would want at least 5e. But it can be quite costly unless you do it yourself and 5e/6 to spec isn't especially an easy fit. But on the other hand it could give you 1GB networking through the house.
The other consideration though is how many devices you have that actually accept a wired network. Not so many IoT devices do and many laptops don't have them any more either.
Without knowing your layout and actual needs, it would be hard to say one way or the other. What probably is worth wiring if you are doing a refit anyway would be any location that might end up hosting your core IT. So broadband routers, switches and servers. If there is a possibility you might move such things in the future then consider wiring to other potential points as well. In a larger house, it would be worth running cable to difficult or remote areas of the building too. That would let you put wired mesh Wi-Fi AP's for example which makes a big difference.
One thing that will always be worth doing though if refitting is installing around about 4x the number of mains outlets than you think you need. Not forgetting to allow for future changes of room layouts.
Also, if you have to choose only 1 wireless network, I'd say always start with Wi-Fi which is the most useful and the cheapest. Then look at Zigbee if you need battery-powered units - though you can probably put that off for quite some time if you took the previous paragraph to heart!
And lastly, maybe consider some 5v wiring if you know, for example, that you need a PIR high up somewhere, having a 5v supply gives you lots of nice options. And while you are at it, if money allows, fit Wi-Fi OTA updatable remote switches on all lighting circuits. Shelly's would be a great option though not the cheapest since they are MQTT and OTA compatible out of the box.
You would need to fit grounded mesh or foil on outside walls for that. Probably not an easy thing. I expect that foil-backed insulation will have some effect but unless grounded, is unlikely to be much I don't think (though consult an expert because I am certainly not one in this area). Not sure that you would want the expense of foil-backed insulation on internal walls though would you? The purpose is to reduce heat transmission between the outdoors and indoors. Of course, some of this depends on what country you are in since there may be different regulations.
Incidentally, this is what the ChatGPT AI had to say about the matter:
Whether or not to fit wired networking when refitting an apartment is a decision that depends on a number of factors, including the size of the apartment, the intended use of the network, and the availability of other options.
There are several advantages to using wired networking in an apartment, such as faster speeds and more stable connections compared to wireless networks. Wired networks can also support a larger number of devices and can be more secure, since they are not subject to interference or hacking attempts.
However, there are also some disadvantages to using wired networking in an apartment. For one, it can be more expensive and labor-intensive to install, since it requires running cables through walls and floors. It can also be less flexible, since the devices need to be physically connected to the network.
Ultimately, whether or not to fit wired networking in an apartment depends on your specific needs and priorities. If you need a high-speed, stable, and secure network that can support a large number of devices, then wired networking may be the best option. If you prefer a more flexible and cost-effective solution, then wireless networking may be a better choice.