You are never going to have a "wired" system if you have a wifi connection in the path. This really isn't any different than hook a USB wifi nic to your PC but you are using ethernet instead. It is still a wifi signal between the room and the router.
For a NAS this likely is the only way you are going to get a wifi connection. Just be aware of the wifi in the path to the router.
I am too lazy to read the manual for you so you will have to check on the details

.
The function you need to make this work is called WDS. Not all devices support this and some you must activate it. So check your Fritz box to see. The d-link boxes likely support it. If this was a simple repeater I would say it will work BUT when you have mesh stuff involved that may not be true. Some manufactures have rigged their equipment to only talk to their own equipment. Mesh systems tend to not be compatible between vendors. They all have their own implementations. Not sure if this is to force you to buy their equipment or something else.
What you need to check for is that the tplink units you have will function as a simple repeater using WDS to the main router. If it has a setting for client-bridge that is even better. It will then not actually retransmit the signal into the wifi and just connect via the ethernet ports.