Apple TV Gen4 is slow to start up

You are using a cable to facilitate a wired connection between ATV and router, you would no longer be connecting over Wifi. When it works over ethernet then that goes to confirm an issue with the wireless connection. Those symptom that are described are typical when there are issues, like interference, over a wireless network. It is not isolated to the Apple TV, and could easily happen to any device connecting over a wireless network.

The fact remains that you are choosing to assume that the issue is with Apple TV. However, you have done nothing to show proof that your wireless network is working at an appropriate level, and the vast majority of users have it working over Wifi just fine, including regular testers on the forum.

There is nothing wrong with having it wired, and if that is what you want to do then that is fine. However, if you wanted to use it over Wifi then you would need to properly investigate the issue within your Wireless network.

Apple TV Gen4 is slow to start up

Wake from sleep for the Apple TV should be in the order of 12-13 seconds. Your TV might take longer than that.

Startup from unpowered to powered and ready, should be in the order of 18-19 seconds.

I've tried all kind of reset/update .. but nothing works.

Does that include a reset to factory settings? Try that. Reset or restore your Apple TV to its factory settings - Apple Support

It takes forever until the app starts.

So … you are not talking about the device itself? Which app is that, that takes forever to start?

None of that rules out your network, and a reset isn't going to overcome such issues. You simply confirmed that the issue goes away when using it wired, and then used an assumption to pass the blame onto the Apple TV, when in fact it is working just fine for the vast majority. If you investigated further i'm sure you would get confirmation on the issue within your wireless network.

Then that would confirm an issue within your network.