The opposite - you should get your router as far away as possible from your components. Routers emit noise.
Ethernet cables make a difference. I’ve tested several and they all sounded different. I tried Supra, Supra with Telegartner connectors, LinkUp from Amazon (very decent by the way), Purist Audio and Audience (mu current cable).
DH Labs cables are excellent value and they’re a good entry point into higher quality cables. If you want to go cheap get Linkup.
https://a.co/d/elkT0FX
Then save up and upgrade to something in the $500-$1000 category.