Two networks over one UTP cable

I have a networking question. I have only one UTP cable between two rooms, and two networks I need to get through that cable.

Bedroom

1 rasbery pi (no wifi)

1 tv setupbox (provided by my ISP)

Main room

1 router (provided by my ISP) with two networking ports - Port A for WLAN - Port B for TV

1 10/100/1000 switch (coected to routers port A)

1 NAS (coected to switch)

I only have ONE UTP cable between the two rooms, and adding another would be a PITA. RasberyPI (a very old one) also does not like any wifi dongles I give it. (did not know support was so bad :/)

If I plug the UTP cable coecting the rooms into Routers port B (for TV), and add a switch in the bedroom and coect both the rasbery pi and the TV to it, the TV will work. My PI will get an 93.XXX.XXX.XXX IP address. The PI is (expectedly) unable to find a path to my NAS.

My inteal network works on the 192.168.1.XXX namespace.

Note: I have no control over the router - port forwarding and WiFi password management is done on their online dashboard.

I've called my ISP. They said they can push the TV into my LAN, but that would prevent me from watching HD chaels and would get bad quality overall. They've advised me to either use a second cable or put it on wifi.

So, is there a solution to my problem that is cheaper/simpler/quicker than laying another cable or ordering a PI compatible wifi dongle online (and waiting a few weeks for delivery)?

What happens if I just plug Routers port TV port into the switch? Since the setupbox relies on DHCP, will it be able to find the right network?

( I should note my networking knowledge is quite limited)