Thank you .Kure again for your help. In the meantime, I have reset the device in two different ways (via GUI and Telnet). Both have not helped. I have also been able to rule out various clients as the cause of the problem by deactivating them.
I also tried "Merlin". Really very cool thing, but it didn't help either.
Finally, I called ASUS support and they are leaning towards a hardware fault. I'll probably get a new ac68u or ac86u now. Merlin" will most certainly end up on the new device. Thanks again for the help.

Thank you for your answer and your experience report. The data carrier (NAS) is connected via Ethernet. I have now reset the device to factory settings as recommended by ASUS Support.
That just took a while. Everything is now running again, but I won't be able to give feedback on whether the problem still exists for a few days.
Thanks for the tip about "Merlin". This was unknown to me until now. I'll be happy to test it or read up on it first.

That is quite strange, I have not yet been able to detect any such anomalies, but I am using the firmware from "Merlin": https://asuswrt.lostrealm.ca/
As an interim question: Is the data storage device connected to the router (USB port) by any chance?

Addendum: The question concerns the speed when moving larger files via WLAN or LAN within the network. Internet speed is not affected.