i've never seen a tv with standby mode..
however i have seen several newer models with auto power off after 15mins if they dont have a signal.
there are a few ways to approach this, some depend on the the tv.
1. use a toggle switch to power tv's power, tv must come on after power loss
2. desolider the tv's power button and wire it to a momentary contact switch.
3. if the tv will power on after a power loss, you can wire up a relay to the pc's power supply, or get one of those smart power strips.
4. disconnect the IR reciever, cut a hole in the screen bezel and move the IR to it.. this way you can use the TV's remote though the monitors plexi/glass, retain full control of the tv.
i believe some also have wired the tv's power to the computer in a way to control but i dont know the details of it.