Easiest way to screenshare/video call without PC

We're looking to setup video calling/audio and screensharing on a TV without the need to plug into a laptop. Ideally we'd like to keep this under £1,000 for the budget.
We've been looking at solutions like Zoom but it looks like the controllers/webcams require these to be plugged into a laptop which is pointless when you can just get a TV, HD Webcam, Wireless keyboard and mouse and a Intel Nuc or Laptop by the TV?
They'd also like to be able to screenshare.
Our idea would be to just do this as a ChromeCast setup and a Yealink Conference phone which would dial into Zoom for the audio. Screenshare from the users laptop via Zoom and then also cast this to the TV using ChromeCast.
Can anyone come up with any solutions for this. Ideally under a £1,000 budget.

How about a wireless display adapter rather than chromecast? - Buy Microsoft Wireless Display Adapter - Microsoft Store en-GB