We have the same FritzBox, also with fiber optic (300), and we are also dissatisfied with the Wi-Fi. The connection itself works perfectly, we have wired most of the LAN sockets and they deliver a solid 300 from the sockets.
Wi-Fi is also fast near the FritzBox, but as soon as we walk through the hallway into our living room the connection constantly drops. Mobile devices then constantly show the "No internet!" exclamation mark on the signal icon. We also had the PS4 connected to the network via Wi-Fi at the beginning. When it connected, it worked reasonably well, but sometimes it couldn't get any Wi-Fi signal at all or could only pull data very slowly. The FritzBox is basically 4 meters straight-line distance from the PS4. Unfortunately, there is a solid wall in between, and possibly the heat pump that's exactly in between interferes as well. Or the underfloor heating. God knows what. In the old house, we never had such problems; there, one FritzBox really covered almost the entire house with Wi-Fi.
Anyway, we have now connected the PS4 via LAN cable, and it runs incredibly fast now. Upstairs we have an access point (Unify) connected via LAN socket. It runs reasonably well, but even there I often lose the connection in the bathroom (also only 3 meters line of sight). Either my phone is faulty (I think my husband does not have such major problems), or it’s the house. My husband does occasionally have Wi-Fi problems but not as often as I do. In the basement, I suspect that the FritzBox is simply not very advanced when it comes to Wi-Fi. We will probably buy a second Unify access point soon and just turn off the FritzBox Wi-Fi. It can’t be my phone, since the printer also runs on Wi-Fi and we had extreme problems connecting it initially because the signal is so weak.