Worth to use audio-grade ethernet cable for portion of the signal path? And what is the exact signal path in my setup?

I did some of my studies at the French national school of telecommunications. I agree with you and… disagree with you lol.

The wire quality can’t help make the bits better. But each ethernet frame (that’s the french name, packets was for X.25 protocol, when we were young lol) is checked. There is an hash function and the “sender” calculate a CRC (Cyclic Redundacy Code) - guess now it’s 32 bit, the receiver calculate the CRC. If they match, banco, if they don’t, the frame is rejected and has to be sent again which can cause jitter. This is simplified as my brain isn’t what it was 35 years ago, and ethernet has improved.
The slower the connection is,the more the jitter is (the upper the speed is, the faster the frame goes from the sender to the receiver which diminish the jitter). The higher the frequency of the cable is, the higher the speed is.
And the shielding is also to take into account. I don’t think a heavy shielding adds a lot to a LAN. But the higher the category of the cable is, the heavier the shielding is, making the cable stiffer. Build your lan becomes tricky when reaching an angles. But for players on boxes, Cat. 8 is almost a must.
So I agree with you, the CRC detects most errors so the wire quality wont make bits better. BUT in packetized world, I thing there are timing issues. Much less now that we have switches (be cautious about configurable switch), even less if switches are upgraded with a better clock. What I wrote might be full of errors but when I was a student, the CRC was only 4 bits. For music, I would recommend class 6A or 7 OCC if unexpensive otherwise OFC as cable, silver plating is a great way to loose money with ethernet cables and would advise against “no tools” plugs… Crimped ones prevent some issues