TLDR since I ended up writing a bit of a book;
LibreELEC 12.1.1 on an Odroid C2. If the Odroid is powered up before the projector, Kodi does not display on the projector but the boot screen instead. If the projector is powered on first, Kodi displays normally.
To be perfectly honest up front, this is not a critical issue, but I am generally curious if it is one that could be solved. First, the quick background. When I built my home theater back in 2015, I was using LibreELEC on an Odroid C2 as the primary media player. Worked great, but I eventually moved on to a Shield Pro for some of the other features, and the poor Odroid just sat in a corner lonely and neglected. Fast forward to today, and needing to replace one of the cheapie AtmosFX window projectors I use during the holidays, I grab the trusty old Odroid and a cheap projector (HY300 Pro which turned out to be a bit of a mistake, but I'm stuck with it for now) and get to work.
My first attempt was using DietPI with a service that would just access a share on my NAS and use MPV to loop through the videos. Unfortunately, getting hardware decoding to work with MPV is nigh impossible, and software decoding was sending the CPU into the 70s temp wise. So for my next attempt, I decided to go back to the old reliable LibreELEC Kodi, and just send a looping play command. This seems to be working great, but it's when I went to automate I discovered this little bug. First idea was to use CEC to power up the projector, but that turned into a nightmarish challenge, and even when it worked, the issue appeared. The Odroid boots, Kodi launches, starts looping the videos, and the CEC call is sent to the projector (which seems to be hit or miss if it works). I then have to use ADB calls to switch the projector input, but that's another story. Once the projector is on the HDMI input, it displays the boot screen, sometimes with or without the LibreELEC splash, but I can see the boot text in the upper left. To date, nothing I've found short of restarting Kodi with a command from an SSH session (or knowing the exact keypresses to get to restart menu) will get Kodi to display. If the projector is already powered on before the Odroid boots, there's no problem (even if it's not already in the HDMI input).
In reality, this isn't much of an issue as I can use Home Assistant to send the IR command to power up the projector before powering on the ODroid (using a zwave plug for that), but I'm curious to understand what's causing it, and if there would be a programmatic fix. I'd love to just have the Home Assistant automation power on the Odroid and everything else takes care of itself, but I can get around it.