HDMI CEC and display power
HDMI CEC is the feature that lets a connected device (your Amazon Signage Stick) tell the TV to turn on or off. CastHub uses CEC for the Wake screen and Put screen to sleep commands. If those commands are not working, the cause is almost always CEC.
What CEC is
HDMI CEC (Consumer Electronics Control) is a small set of HDMI standard signals that lets HDMI devices control each other. It has been part of the HDMI standard for years, but most TVs ship with it disabled or under a brand-specific name.
What it is called on your TV
Anynet+ on Samsung. Bravia Sync on Sony. SimpLink on LG. EasyLink on Philips. CEC, HDMI Link, or HDMI Control on most other brands. Open your TV settings and look for any of these.
Enable it
Turn the CEC feature on. Some TVs also have separate sub-options for power on/off; enable those too. Save the setting and reboot the TV once if it does not take effect immediately.
Test it
From the CastHub web app, send a Wake screen or Put screen to sleep command to the device. Check command history; the command should complete and the TV should respond within a few seconds.
If it still does not work
Some older TVs and some commercial displays do not support CEC at all. Some require the HDMI cable to be plugged into a specific port (often labeled HDMI ARC or CEC). Try a different HDMI port. If your display does not support CEC, display power commands cannot be used; consider using a smart power strip or a CEC-injecting HDMI adapter for that screen.