It's very unlikely to find someone with the same hardware here, who solved your issue. The driver of your case display works for most of the output, so I bet it's a driver problem (not fully compatible to your display).
If you have programming skills, you could try to find the source code of the LCDproc add-on, and adapt it for your needs. Because your hardware is quite exotic, I think that's your only option.
OK, then I'm running out of ideas, too. Maybe you still have guarantee, and get a replacement. Try it on a friends TV before you replace it.
Download a full Linux, like Ubuntu, and run it in "live" mode. If everything works, look for the loaded driver modules, and try to load them on LE.
I think that's a good way to figure out the usability of an "old laptop".
Thanks for the tests. I compared your guisettings.xml to mine. I found a difference, which could be the cause:
<setting id="audiooutput.dtspassthrough">true</setting>Set this setting to false.
LE creates symlinks for all mounts. Some services can't go beyond such a symlink.
chapas :
Does it work if you define two separate buttons instead of one switch button?
Activate "HDMI and Analogue" sound, and test analogue output on RPi's headphone jack.
Disable I2C and UART for testing.
Make sure your HDMI cable is HDMI 2.0 or 2.1 standard (ready for 4K).
<setting id="audiooutput.channels">8</setting>
Set it to 2.
chapas :
It's a usual error that the RC generates multiple events, but you only need one event when you press "g".
You can fix it by changing some timings at the CEC adapter settings.
Go to Settings -> System -> Input -> Peripherals -> CEC Adapter.
Then edit the timings like this (example from my settings, last three entries):
PS: Sorry, I've just recognized you are using a keyboard, which makes double triggers unlikely. The error log says that a JSON call can't be executed. The call wants to change this line at /storage/.kodi/userdata/guisettings.xml:
<setting id="lookandfeel.soundskin" default="true">resource.uisounds.kodi</setting>
Make sure you are using the default skin.
You can't pass-through A/V signals on RPi, but you could trigger an HDMI relay when the RPi turns on.
If your RPi is always on, you could write a script to trigger the relay by RC.
PS: I know that so called "sharing switches" exist for USB. They automatically switch to the active source. Maybe switches like this exist for HDMI, too.
Router - ZyXEL Keenetic Ultra II, no 2.4, only 5GHz...
I remember that other RPi 4B users have the same problem with 5GHz WiFi. Because it works with the same Hardware (same RPi, same PSU) on Raspbian Buster, I assume it's a bug on LE. My guess about the bug is that LE uses a different energy management. 5GHz needs more energy than 2.4GHz. Maybe write a bug report to give the bug more attention. I think that's all you can do.
Just a little explanation: On a Linux OS like LE, the OS selects the the eGPU (your Nvidia) as default. It seems like the driver for your eGPU is not available, so the OS switches to the iGPU (your Intel). If you really think it's worth to go into depth, provide a log file.
If you are running the same add-ons on LE and CE, then one of those could be the problem.
Your benefit now is to have one device for testing, and the other for "production". 
Run a vanilla installation. If you don't have issues for a couple of days, add one add-on, and test for a couple of days again. Do this for each add-on. Hopefully you will find the add-on, which crashes the OS.
Is there a way to just add this functionality to the default skin?
Sounds like a feature request. 
PS:
It's important to understand that power-off on RPi doesn't lead to a stand-by mode, as you know it from other devices.
The RPi can wake up other devices, but not vice versa.
USB and HDMI ports will not respond to any signals after power-off.
Your only option to power-on while connected to power supply is to use the GPIO.
vtsteez243 offered the best solution, go for it.
You still haven't understood what we are writing here.
What you want is technically impossible.
HDMI-CEC can't turn your device on.
The specs say that you have 1080p, so you were not correct at post #3.
That's a game changer. It means, not all available video modes are detected by LE.
Now my suggestion is to check your HDMI cable. Try a different cable or buy a new one.
You need an HDMI 2.0 or 2.1 standard cable be future-proofed for 4K.
Don't be sure you really used 1080i on OpenELEC, because your TV has 1080p.
It is correct, but it doesn't help. Your TV is "HD ready" standard.
According to this it's very difficult to deal with interlaced video modes. So I think Kodi has good reasons not to support interlaced modes.
Maybe you had real interlaced modes on other RPi OS'es, but on LE (and other multimedia OS'es) your chance is very low to make it work.
