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Good job. when you get a chance, plug in the HDMI cable and see if it also has video. You can always go back using the DP cable. Actually DP is the better way to go but it will rule out having a dead HDMI.
I doubt it's "dead", but perhaps just ill? Disabled?

I am curious is the "problem" is the monitor's HDMI port, the mini's HDMI port, or simply a compatibility issue.
 
I doubt it's "dead", but perhaps just ill? Disabled?

I am curious is the "problem" is the monitor's HDMI port, the mini's HDMI port, or simply a compatibility issue.
It's all of the above and that is a handshake issue. There is a timing sequence where a signal is ready for output and the monitor is ready for the signal. When the timing is off, the signal breaks so it results in NO signal. It's not uncommon with HDMI.
 
I've been using a Belkin USB-C to Minidisplayport cable for my 32" BenQ QHD screen on my 2018 Mini for almost three years, never any problems. But recently I wanted to connect another USB-C SSD to my Mini full-time, so I changed to an HDMI to HDMI cable instead.

And something interestiing happened when I did that. My Mini boots much faster with the screen connected to HDMI instead of USB-C. It was taking a long time to boot the Mini with multiple external SSD's connected, the desktop would appear in about 30 seconds but then it could take quite awhile (another 30 seconds or more) for disks and folders to appear on the desktop.

That just doesn't happen with the HDMI monitor connection, the complete desktop appears in under 30 seconds now, the difference is quite dramatic. I suppose this has something to do with the bandwidth needed for the screen as well as the external SSD's? Anyway, I was quite surprised (and pleased) to see the difference.
 
I had same concern upgrading my mac mini from macOS 12.6.3 (Monterey) - Here is my setup:

Primary monitor (with menu bar) is LG 27UL550-W 27" 4K connected via Monoprice HDMI cable.
Secondary monitor is LG 27UD58P-B 27" 4K connected via Cable Matters USB C to HDMI cable.

First I rebooted the mac mini to clean out any cobwebs on the system prior to running the upgrade. I run my monitors with sleep disabled (and a screensaver) due to all the monitor wake issues. I just have to manually turn off the displays when I'm done for the day.

I initiated the upgrade to Ventura. At first the primary display turned off (like it was in power saving mode) and the secondary display had an apple logo. I let it be these way for a couple hours, came back and found neither display was on but the machine was running.

I tried unplugging HDMI and USB-C cables from back of the mac mini a few times, waiting 30 seconds to plugin them back in - but it wouldn't wake up the displays. Tried turning displays on manually, changing inputs back and forth, nothing would wake them.

Finally I tried moving the USB-C end of the HDMI cable from its usual port into a different port on the back of my mac mini, and 10-20 seconds later I heard my external HDD spin down and the mac mini power cycle. It came back up again with the apple logo on the secondary monitor, this time with a progress bar. Within 15 minutes or so the upgrade was complete and I was back to having two working monitors.
 
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