I would need a device to replace the rj45 cable that runs through my flat. Basically the idea is to remove the cable and instead plug in a wifi device to connect my computers to (my wifi network is quite powerful and serves the whole flat). Does this router fulfil this function?

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You need a device to connect your computers to the router via Wifi instead of via Lan cable? -> Access Point Device
You can set the Asus RT-AX58U router to access point mode: https://www.asus.com/ch-de/support/FAQ/1015009/ But you don't really need a router for this, a simpler device can also do this: https://www.digitec.ch/de/search?q=access+point&is=acces Alternatively, you can also connect your computers to the router via the mains using a powerline device.
But I am not sure if I have understood you correctly.

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I would need a device to replace the rj45 cable that runs through my flat. Basically the idea is to remove the cable and instead plug in a wifi device to connect my computers to (my wifi network is quite powerful and serves the whole flat). Does this router fulfil this function?