Thanks to your explanation, I hope I'm finally starting to understand. When I turn on the TV using the Samsung TV remote, the screen is black just as when using the Roku remote, which agrees with what you have been saying about the power button on the Roku remote turning on ONLY the TV.
When I press the HOME button on the Roku remote (which I refer to as "remote" from here on) after the TV is turned on, the Roku home screen appears, just as you wrote, and from then on everything works perfectly.
The thing that confused me is that the Streaming Stick 4k and the Ultra seem to function differently. The Streaming Stick 4k functions exactly as I would expect; the Roku home screen appears immediately after I press the power button on the remote. I don't have to press the HOME button after I turn on the TV. The function of the blue light on the Streaming Stick 4k also makes sense; it turns off when the TV is turned off and stays off. I'm not so sure a blue light that stays on is a positive feature, even if it might not be a big issue. In a dark bedroom, even a small light can be pretty bright and annoying if you are someone who takes time to fall asleep (which isn't me, USUALLY).
I disabled the TV's HDMI CEC.
I initially turned of the screensaver completely.
I then set the screensaver to turn on after 10 minutes. None of these steps had an effect on the blue light.
It still doesn't make sense to me that if I turn on the TV with either the Samsung remote or the Roku remote before the Ultra has turned on the blue light, the Roku home screen shows up immediately. When the TV is turned on and the blue light is on, I get the black screen. It seems that when the TV is turned on with the blue light off, the black screen should appear because the Ultra should be in "sleep" or "standby" mode, which is opposite of what occurs.
I'm beginning to think that there is an error in the software that causes a mismatch of the illumination of the blue light and mode of the Ultra.
It seems the Ultra has two modes, an "active" mode for which the Ultra is capable of streaming, and a "sleep" or "standby" mode for when the TV is off. Currently, when the TV is on and the Ultra is streaming normally the blue light is on, which makes sense.
Currently for the Ultra, when the TV is turned off, the blue light turns off initially and then turns on after a short time. It seems like this is opposite of what should happen. It seems that when the TV is turned off, the Roku stays in "active" mode for a short time as the TV can be turned on again and the Roku home screen appears immediately. It seems like the blue light SHOULD be ON for this time, but as it is now, it is off. A short time later, when the blue light turns on, the Ultra evidently switches to a "sleep" or "standby" mode, and the TV shows a black screen when it is turned on alone. This is when the blue light SHOULD be OFF.
This is what I think the software should do:
When the TV is turned off with the power button on the remote, the Ultra should remain in "active mode" (capable of streaming) for a short time (as it now does). The software should recognize that the power button has been pressed (just as it recognizes that any other button on the remote has been pressed) and start a timer that counts down after which the Ultra switches to "sleep" or "standby" mode. The blue light should remain on during the countdown.
When the countdown expires, the Ultra should switch to "sleep" or "standby" mode (as it now does), and the blue light should go off.
When the Ultra is in "sleep" or "standby" mode, pressing the power button on the remote should both turn on the TV and switch the Roku to active mode.
Perhaps the Ultra can recognize a signal on the HDMI port to determine if it should be in "sleep" or "active" mode instead of using a software timer, but right now, when the power button is pressed and the TV is turned on, the Ultra does not switch from "sleep" to active mode; another button on the Ultra must be pressed to switch modes. So, maybe there is no such signal.
Thanks for your help, which has taken more than a small amount of your time. I hope your explanations can help someone else. I have seen other posts that describe problems similar to mine (especially with the blue light), with no conclusive explanation or solution, so your explanation is much appreciated.