If it’s cable internet and not fiber/DSL, I’d look at connecting the ISP’s coax to the house’s coax. Provided all of the house’s coax ports are connected to a splitter, you could feed the ISP coax into the nearest port and plug the cable modem into the office port.
You can’t connect any Bluetooth audio to the PlayStation (Source: Sony). You “can” use a USB Bluetooth dongle and pair to that, but the experience isn’t great with audio latency.