Poor WiFi in the new building despite fiber optics

What the FRITZ!Box displays is one thing, what arrives on your devices via WLAN is another. Therefore, please open a website with a speed test on one device and post the data here.

With us, the Fritzbox in the HTR also has almost no range inside the house. Only an access point, in our case Unifi or 1750e, connected via LAN in the attic solved the problem.

Since there are still network sockets in the house, simply install additional access point(s) there. It should be clear that the Fritzbox cannot have range (and certainly not in the 5 GHz range). Electricians usually have no clue about this. That's where statements like "everything is over WiFi nowadays" or "one access point is enough" come from. If you plan properly, there are LAN cables on the ceiling with Keystone in a small box. Then an access point is mounted on that. For example, Unifi nano HD. Specifically at the places where you have the most devices and need the most speed. For example, living room, office, children's room... Everything that is rather stationary and has a LAN port is connected by cable. Yes, don't do mesh. You have network sockets. So don't build a crutch.

Your headline sounds like: "Our internal mail is slow, even though I order everything express." Do it like and others recommend and get someone to help you. Whether that is a fairly knowledgeable friend or a professional doesn't really matter.

One should not make a science out of everything. Fritze central, one or two more repeaters or mesh and everything is fine. If you forgot the network sockets, then a workaround via powerline and repeaters. There is always a solution.

You mean APs, right?