You may not get the improvement you want using a LAN Cable, so I don't want you to spend a lot of money doing so. Initially you are only wanting to test to see if the WiFi connection is wanting. Do you have another TV nearer the Router that you could try just for testing the Roku/Spectrum with a LAN Cable you already have? You could even use a Computer Monitor (with an HDMI input) for testing purposes.
"CAT6 is the sixth generation of Ethernet cabling used in business and home networks and the current “typical” cabling standard used in modern office buildings. CAT6 is backward compatible with CAT5e and CAT5 standards that came before it. These cables support Ethernet data rates of up to 1 gigabit per second. CAT6 cables can also accommodate 10 Gigabit Ethernet connections for a limited distance of about 55 meters.
Category 8 is the official successor to Cat6A cabling. It is officially recognized by the IEEE and EIA and parts and pieces are standardized across manufacturers. The primary benefit of Cat8 cabling is faster throughput over short distances: 40 Gbps
up to 78’ and 25 Gbps up to 100’. From 100’ to 328’, Cat8 provides the same 10Gbps throughput as Cat6A cabling.
CAT5e cable can transmit 100 Mbps
Ethernet at a distance of 100 meters
I don't know how many feet (or meters) your Sony TV is away from the Router (?) but I really doubt it is over 100 meters or ~300 Feet!
So you should be able to use Cat5e
as the maximum output of the Roku is 100 Mbps
. Of course if you get a deal on CAT6 / CAT8, it'll future proof you for other applications a bit.
I've forgotten where you live (?) but you should be able to find LAN cables pretty cheap at Monoprice
if you are in the USA. ($10 / 50 feet or $20 for 100 feet with terminations already on each end. I typically terminate my own cables.) You may be able to get something even cheaper on Craigslist or Facebook Marketplace.
Good luck with the testing.