I ran another series of tests without the Sony Bluetooth headset connected, but with the USB flash drive attached. The cursor lag did indeed disappear when I switched monitors. Good catch.
I also found that the USB flash drive made the lag significantly worse, especially when connected to the outermost USB-A port on the Mac mini.
Test results :
Iiyama monitor, without the Bluetooth headset
I performed several test cycles with three different configurations.
1. Mac mini with no USB drive
There was barely noticeable cursor lag during the first test cycle. I could not reproduce the issue during the subsequent cycles. So, no issue here.
2. SanDisk USB drive connected to the outermost USB-A port
This is the rightmost USB-A port when looking directly at the back of the Mac mini. It is also the port I normally use for this drive.
During the first test cycle:
Cursor lag was severe.
The mouse stopped responding for approximately 20 seconds, then recovered automatically.
The USB drive disconnected by itself and did not reconnect automatically.
The following test cycles were only slightly better, although the USB drive remained connected.
3. SanDisk USB drive connected to the USB-A port closest to the HDMI port
During the first test cycle, I noticed only minor cursor lag while the Sound panel was open. It was not particularly disruptive.
I could not reproduce the issue during the subsequent cycles. It works properly.
ASUS ProArt monitor
I then connected an ASUS ProArt monitor using the same HDMI cable. No headset.
I could not reproduce any cursor lag, even with the USB drive connected to the USB-A port that had caused the most severe problems with the iiyama monitor.
Additional information about the iiyama monitor :
The iiyama monitor already has significant HDMI reliability problems when operating at 4K 60 Hz.
In my experience, neither the Mac mini nor other computers can reliably wake it from standby. I have to power-cycle the monitor before it will detect the video signal from a computer connected to its HDMI 1 input.
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The place to file bug reports is Feedback Assistant (the app), or you can use the web interface at https://feedbackassistant.apple.com
Thanks, I submitted a report through it shortly after creating this thread. I was not aware of that option when I originally posted.