Reporting back for future generations, I think I've found the issue. I was retracing my steps and found this:
When installing postmarketOS there is a device specific instructionto run "fastboot oem uart enable" command.
So I tried to run "fastboot oem uart disable" and then flash UT.
So far working like a charm. Did a switch off, did a restart and all works as I'd expect it - also with Libertine set up.
There is Lutris or Faugus launchers that you can run Battle.net from. Would be interesting if this would work via Libertine.
Reporting back for future generations, I think I've found the issue. I was retracing my steps and found this:
When installing postmarketOS there is a device specific instructionto run "fastboot oem uart enable" command.
So I tried to run "fastboot oem uart disable" and then flash UT.
So far working like a charm. Did a switch off, did a restart and all works as I'd expect it - also with Libertine set up.
@arubislander well thanks for trying. It's weird indeed because I had no issues first time around.
Well at least I know to not try different OS after installing UT I guess.
@arubislander
Update channel 24.04-1.x/arm64/android9plus/stable
Build number 24.04-1.2
@arubislander yeah. When I go to recovery mode and reboot from there, the device start as expected and I get to Lomiri environment. Though this is not working 100% - for example I tried now and got into a reboot loop again 
I'm trying to find a pattern and while rebooting from the recovery mode (I'm in recovery and click on "reboot") works most of the time eventually, it's not all the time. Makes no sense to me.
@arubislander I was not sure which checkboxes you meant so I did a full reflash again. Here is how it went:
Flashed back to Android (forced flashed all partitions under advanced options, sounded like a good idea).
UT flashing stable, checked wipe userdata and bootstrap (there were no checkboxes except these two so I assume you mean these)
Restart shuts down device, no reboot.
Now it just shuts down instead of getting into a reboot loop.
Getting UT splash screen - white screen - UT splash screen again - screen dims then turns off
Reboot from recovery mode goes to UT splash screen then reboots and shuts down.
Factory reset, left the device be for a while.
Took it a while to start, but this time selecting restart actually rebooted the device - but shut down after UT splash screen.
Left the device off for some time, booted fast and as I'd expect a mobile to boot up.
Restart actually reboots, though it took his sweet time booting up, got stuck on UT splash screen.
Reboot from recovery mode worked well, no hiccups.
This is without Libertine set up.
@arubislander I did, flashed the required Android 9 version over postmarketOS. When the issues started, I tried flashing UT again on the existing installation, as well as flashing Android and flashing UT again.
So I recently bought Pixel 3a to try the waters of Linux mobile. I installed UT first, but I wanted to try others as well so later installed postmarket OS. While I liked it, UT functioned bettet so got back to it. That's when the issues began.
Now when I restart, it sometimes reboot but usually just shuts down. When it reboots (or I boot it up) it gets stuck in a loop:
Boot -> google splash screen -> UT splash screen (rarely it doesn't even reach it and reboots after google screen) -> freezes (sometimes I get white screen or just flashes of white screen) - reboot - repeat.
This gets way worse with Libertine set up - it goes through after a number of cycles, then just gives up and finally doesn't reboot and stays shut down. And when I have a package installed in Libertine (tried with Firefox) it feels like it gets worse still and I'm unable to get to login at all.
Rebooting through recovery mode usually gets the device to fully boot up successfully. Did factory reset and also tried flashing UT again, issues persist.
Not sure if relevant, but when I was flashing UT the second time around, the installer didn't register the device automatically, had to select manually.
Weird thing is it worked fine the first time - but after I tried postmarketOS and went back again is when the trouble started. Not sure what I could've done wrong though and no idea how to troubleshoot. I'm pretty new to Linux, very much on a regular user level.