I'm having similar problems just using the screensaver.
For whatever reason, when I first tried, waking the TV worked if I pressed the OK button twice and it would open to the screensaver, turn off the TV again, and the second time I pressed OK twice, it turned on and stayed on. Then it never did it again. I'm on HDMI port 1 on my TV and using a Nvidia Shield remote on a RPI4. Rebooting did nothing.
That was with the Aerial screensaver...
Powering on the RPi powers on the TV. Going idle for a minute turns the screensaver on and powers the TV off.
What screensaver are you using? Using Aerial, I can't get the screensaver to come on if I have a movie paused, but I can if I use the black screensaver, which for whatever reason flickers between a light and a dark black, but that one doesn't turn off the TV at all if I'm in a movie. If I'm not in a movie, the black screensaver does turn off the TV. A single press of the remote does turn on the TV now.
So, results are:
-Not in a movie, with Aerial, screensaver turns off the TV but can't turn it back on
-Not in a movie, with black, screensaver turns off the TV and I can turn it back on
-In a movie, with Aerial, can't get the screensaver to turn on at all
-In a movie, with black, can get the screensaver, but it never turns off the TV.
I'm using the CEC settings to turn the display on and off with the screensaver btw. Maybe it's relevant, but in Settings/System/Input/Periperals, I have two CEC items and for the sake of consistency I set the values to be the same on both. I don't know why they're there or if they're conflicting, but maybe that plays into things somehow. After I set the settings on both, the second one shows up in yellow which I assume means it's active.
So yeah, something seems off in Kodi. I can't reproduce your issues , but I've got something similar where I can't get it to wake from Aerial in the circumstance where I'm able to get Aerial to turn the TV off. And I'm not able to get the screensaver to turn the TV off when I'm in a movie and the screensaver comes on.
So I tried your settings a little bit.
I tried setting the black screensaver to 6 mins and turning off the display after 5 min idle. The result I got was no signal displayed on the TV and not turning it off. I waited till the 6th minute to see if the screensaver activating in Kodi would then turn off the TV and it didn't. A single button press on the remote woke Kodi up.
Then I tried disabling the setting in the CEC config that turns off the display with the screensaver and like you, tried getting a black screensaver after a minute and turning off the display after 5. After a minute, I got a flickery black screensaver and 4 minutes later, Kodi killed the display signal but didn't power off the TV. Back to the "no signal" message on the TV.
Something is very inconsistent. I don't know if verbose CEC logging would turn up anything. It's particularly noisy and it's not like Kodi is failing to send the signal properly, it's just not sending it at all.
Anyway, hopefully this helps someone. Maybe it's time we attach some logs...