Not all Fritzboxes are the same, so you need to know which WLAN standard your Fritzbox supports. The ASUS router supports WLAN up to AC and would then support max AC or WiFi 5 as a repeater if Fritz brings AC. However, at least a 50% bandwidth reduction must be accepted in repeater mode. In addition, the clients must always register again when they switch from the Fritzbox to the repeater, or vice versa.
Today, mesh configurations are used to avoid the disadvantages of repeaters. You are always in the same network and the transition is seamless between the mesh points and the router.
I myself am a Swisscom Access customer and have set the Swisscom Internet box to "DMZ" (allows everything through unfiltered) and placed an ASUS GT-AX11000 router behind it, which takes care of the routing, static DHCP, port forwarding, etc. I also have an ASUS GT-AX11000 router. etc. Three AX92U mesh points with Ethernet backhaul are connected to it. The whole thing supports the AX standard (WiFi 6) with WPA 3 authentication. That's where the action is.