If your computer is close enough to where the Tv is; you could probably use OBS to create a multi-view output. From there you would output it from your computer to the TV. There are number of ways to connect to a TV with an HDMI to HDMI cable being the easiest.
OBS Studio is a free piece of A/V software that is extremely popular; especially among those who livestream. You do not have to livestream to use its features.
If Nest will not allow you to have a single multi-camera view you should be able to add three separate web pages as sources and just drag them onto your screen and adjust the size and shape of each view on the single output.
It will probably look a lot better with an even number of cameras (2 or 4) for a multi-view output.
https://obsproject.com/After you get OBS setup and looking like you want its easy to get a monitor out. Just "Right-click the Preview windows and choose "Full Screen Projector Preview" and select the monitor you want to output the full-screen preview to" it will have a list of all monitors and displays connected to the computer. Pick the TV.
You can test this feature with just regular websites before you go out and spend any money.
I hope everything is going well people usually do not just wake up one day and decide to monitor their employees via camera.