Ethernet to bridge router, versus straight to main router

Howdy all, I wanted to get some confirmation as I’m not well versed in networking.

Recently switched to fiber, so the location is different than where our modem is. I’m currently running a 50ft Cat5e cable to my desktop, connected to my old router that is now in bridge mode. The new router is an Eero 6+ and the old router is a Nighthawk that has gigabyte ports as well.

Before buying a new Ethernet cable, I was thinking Cat6 at 75ft, I wanted to make sure I’m on the right track. Is a computer that is hooked up via Ethernet, to a bridge router, essentially the same as going WiFi in terms of speed? My assumption is that even if it is slightly more reliable than straight WiFi, hooking directly to the main router will still provide a significant speed boost than having to wait on the signal from Eero to Nighthawk to desktop.

I’m mainly curious because my desktop is an old i7-2600k, so I’m not sure if the tech being way older is just going to limit my network bandwidth regardless and make it near pointless to buy a new cable and run it all under the house.

Thanks!