The reason your TV doesn't turn on after a few minutes is it enters a deep sleep. You can turn in back on from this state by using a WakeOnLan app. I found a couple for Hubitat and they all work well. Install the app, enter your TV's IP and Mac address, and then map it to your TV's plug switch you created.
If your TV can be controlled using SmartThings, you can also get rid of the plug entirely. This solution does use the cloud to turn it off, so if you prefer local control, keep the plug.
Step 1... Connect your TV to SmartThings
Step 2... Install HubConnect in SmartThings IDE and on Hubitat, and connect the two.
Step 3... Share your TV in SmartThings. This will create a switch in Hubitat automatically.
HubConnect will only see it as a switch, and so you can only share power controls. No volume or input control I'm afraid.
Step 4... Install WOL as above and connect it to your TV's switch.
And now you can turn your TV on anytime
Update. HubConnect now supports connecting to AVRs, and SmartThings will accept the Samsung TV as an AVR. This will allow hubitat to control more functions including changing volume and input. I have not been able to get SmartThings to report current input back to hubitat to use for my automations, but this is progress