I am still waiting for you to describe how you connect to the Internet generally.
All the IP addresses on your home Network are likely to be from one of three ranges of strictly local IP addresses. Those are no good for talking DIRECTLY on the Internet. Your Router 'acts as your agent' on the Internet, and translates those local Addresses to its Own IP address, essentially saying, "when you send the answer, send it to ME, the Router, and I will return it to my requestor ... and I won't tell you to where."
When you set up another local device (easiest to imagine may be a Network Printer) its packets are sent DIRECTLY across only your local Network through local connections, Switched through your Router. The Internet could stop working and you could still print just fine.
When you set up a Networked Attached Storage (NAS) device, its packets will also go through ONLY the Switch function of your Router (or other stand-alone Switches) and be sent DIRECTLY between your NAS device and your computer.
One more rule to remember: Packets going toward the Internet are sent through the TOPMOST, WORKING, Interface shown in:
System Preferences > Networks
You COULD choose to connect ONLY your NAS to 10G Ethernet directly, and NOT through any Switches/Routers. [Cross-over cable is not needed by modern equipment, it all adapts, but all eight wires IS required.] On your Mac, make Wi-Fi topmost. Then Internet traffic can be seen to go over Wi-Fi, local NAS traffic will go where the local IP address of the NAS is available [10G Ethernet] which is not the TOPMOST, but is a WORKING interface.
This setup is not optimized for best Internet performance, but can allow you to understand in a visceral way that your NAS traffic and Internet traffic are not being mixed, and the Internet is not being used for your local File Transfers.
[if you do this, you may need to manually configure your 10G Ethernet addresses if it does not immediately work, but that is a straightforward, one-time process that Readers can help you with.]