Ok, so now you are not using the HDMI port?
Did you apply a macOS update after changing to eGPU? 10.15.2 to 10.15.3 or 10.15.1 to 10.15.2 to 10.15.3?
I my cases which where only fixable by replacing the logicboard at the time of the update the HDMI port was used by a Apple HDMI to DVI Adapter to the display.
I could be that HDMI only breaks if something is connected to the HDMI port during the update.
I still try to find out what happens with the macMini 2018 HDMI port
So my questions to you are:
Did you do any upgrade after changing to eGPU?
Is the HDMI port of your MacMini 2018 still working, if you power down, then disconnect the eGPU, connect a HDMI to DVI Adapter or a HDMI cable using a display which do not search for a signal source?
If you had updated macOS and there was nothing connected to HDMI at the time of the update that it can be that HDMI only breaks if something is connected to the HDMI port during upgrade.
Can you confirm or deny something of that?
Q: Ok, so now you are not using the HDMI port?
A: I am using the HDMI port for an HDMI display emulator. And thus the HDMI port is still working.
Q: Did you apply a macOS update after changing to eGPU?
A: I always had an eGPU and yes I had applied a MacOS update. And one of my monitors is now connected to one of the RX 580's HDMI port.
Q: Did you do any upgrade after changing to eGPU?
A: What kind of upgrade? You already asked about MacOS upgrades in the previous question. As the only user upgradable item is RAM I assume you are asking about this? If so then the answer then is no. It came with 32 GB and still has 32 GB RAM.
Q: Is the HDMI port of your MacMini 2018 still working, ...
A: Yes, see the answer to your first question.
Q: ... if you power down, then disconnect the eGPU, connect a HDMI to DVI Adapter or a HDMI cable using a display which do not search for a signal source?
A: I do not entirely understand the question. Perhaps English is not your first language (your profile is silent with respect to your location). But let me try ... If I connect a display to the HDMI port on the Mini, and boot up, the display turns on just fine. That is what I did prior to getting the emulator plug.
Q: If you had updated macOS and there was nothing connected to HDMI at the time of the update that it can be that HDMI only breaks if something is connected to the HDMI port during upgrade.
Can you confirm or deny something of that?
A: I had a display connected to HDMI when I upgraded the OS. This was before I had the emulator plug.
Hope this helps.