Just sharing my experiences so far, with this issue after many hours of troubleshooting.
Its seems to be affecting anyone that has a 4k display and using HDMI connection.
This issue occurred 1/10 times when I was using mac mini 2018 and Mojave. I never gave it any thought until
after installing Catalina, then catastrophe struck.
I connected a windows laptop to the monitor using the same HDMI cable and all was well.
I immediately reconnected the same cable to the mini, and blackness.
After many reboots and smc resets, maybe it worked twice.
Important!! once the monitor finally displays video output, as long as I don't shutdown the mac mini
I can restart it as many times I like. Picture is always shown on the 4K monitor (LG 4K UD58B)
Once I shutdown Catalina, that's it, no more video output.
The only temporary solution (if you can call it that) is having an old monitor near, connect the HDMI cable
to it, and then switch on the mini. Once the Apple logo appears I can connect the HDMI cable to the 4k monitor
and all is OK.
Conclusion
For me, if buying an adapter, from thunderbolt to HDMI, will fix this issue I'm ok with that.
I'm not a power user/don't have many thunderbolt devices (yet anyway) to be worried loosing one port.
But for many others this could be an issue and I think Apple can fix this in a jiffy.
Remember Catalina has been released less than a week a go and just maybe this issue hasn't caught their attention yet.
Salute