I managed to fix the problem last night.
What seemed to happen caused by the power-outage was that LibreELEC reset some of the configuration - namely the set refresh rate for the graphical output.
Already when I initially set up the system I had the problem that in my setup (with AVR in between projector) for some reason the default refresh rate of 60 leads to that behaviour (splash screen). Only after hooking up the NUC to a monitor (where it immediately works), then setting the output to a different refresh rate (this time I tried 59,x instead of 50 like the last time), it also works in the desired setup. I just forgot this, but searching the forum and finding my own thread reminded me.