Ignoring the sound better magic or not, I was checking up on the specs that have emerged since I retired ( we used fiber almost exclusively anyway)
7, 7a and 8 standards are proposed but will use proprietary connectors. Not RJ45s
Prices on cables have come way down. ( beware of source)
Plain old CAT-5, UTP is of course sufficient for anything in audio unless you need magic .
5e is a little better with bonded pairs. 6 and 6a have a center core for more consistent impedance. 6a is also a little smaller. CAT 5 to 6a may or may not have an overall shield. 6 and 6a may have individual pairs shielded. CAT 6 connectors fit RJ-45 but are staggered pins in the crimp. You are still looking at 10 ee-13 error rates or less with layer 2 fixing any that may happen. TCP/IP is absolutely reliable bit for bit. As with anything, I would not trust Amazon/E-Bay etc that the cables actually meet spec. Unfortunately BJC cables are not shielded but they are tested to spec. So I have no guaranteed source for shielded cable.
So for the paranoid, or want it because it is available, or bragging rights, whatever, 6a shielded is reasonably priced now. I noticed most of the Netgear switches all have shielded ports now. If you believe you need fantastic speeds for your streamer, you can get managed switches so the Internet to your streamer has priority. You can even get a D-link or Netgear switch with a sticker on it for 20 times the price that says "audio quality" It may have a better power supply. If you buy a data-center class switch from Cisco, it may be cleaner.
I noticed the older unmanaged 5 port usually used 5V, but most 8 port and manages switches use 12V. A couple turns around a big fat ferrite will knock any RF off those cables feeding the switches.
I may upgrade as I have a WI-FI repeater and going PoE reduces the wiring mess.
We can measure anything in a data cable. We can't tell you which measurements may cause an audible difference. We can't tell you how well your device ports were executed. We can't tell you how good your Internet MODEM and router are but they can be measured. This is the same in analog cables. We can measure, but that does not tell us what we need to target. Too many unknowns on both ends. Without measurement I can absolutely tell you, no cable can add any detail that was not in the original source. That is magic.