https://www.amazon.com/dp/B00A128S24

Coax in wall -> Modem -> Router -> Internet jack of Switch 1 -> Any port of Switch 1 -> Internet jack of Switch 2

Will the connection between ‘any port of switch 1’ provide internet to the rest of the jacks on switch 4? I assume yes because any traffic will just go through that connection and then be handled by switch 2. Maybe some arguable congestion on that line, but this is for a small (read: apartment) home network that is hardly going to get blasted with bandwidth ever.