This is a learning from a just solved situation and not a request for help or problem solution request. Hopefully it might save someone else from the dope-slap I gave myself.

This morning I was reminded old troubleshooting techniques never die they are just forgotten.

1. THE SITUATION:
   1. The battery would not charge and was rapidly drained to < 7%
   2. All I/O slowed to pre-global warming glacial speed
   3. Launching an app could take minutes to complete
   4. Printers appearing and disappearing
   5. Quit an app and it might leave individual tasks still running
   6. Etc'
2. TROUBLESHOOTING:
   1. Reboots, diagnostic tools, logs, nothing helped.
   2. Then the battery ran down so the mandatory first order of business was to get the power working again which plugging in the Apple Poser supply in addition to the power supposedly coming from the Thunderbolt 3 Dock solved that at least temporarily.
3. SOLUTION:
   • To make a short story even longer, I contacted OWC Technical Support and at their suggestion pulled every connection out of the Thunderbolt 3 Dock, let it sit for a minute or so then plugged everything back in, reconnected the TB3 to the MacBook Pro and disconnected the Apple Power supply. Every problem disappeared.
4. CONCLUSION
   1. A long time ago I learned
      1. anything that effects I/O has the potential of doing lots of apparently unrelated mischief
      2. Hubs and Docks are often not the most carefully engineered devices
      3. A complete power down reset may be the only way to completely reboot/reset a system or accessory
   2. Just because I haven't found the necessity of using a trouble shooting technique in a few years, does not mean it is obsolete or won't work
   3. No matter how many red herrings there are, start with the most serious problem first. (In this case I allowed the on screen issues distract me from the impending shutdown due to the discharged battery.)

And what, pray tell, does this relate to in terms of computer hardware?

The issue turned out to be entirely hardware related. The upgrade to MacOS 10.14.4 was entirely coincidental — which seems to happen frequently.

Which still doesn't answer the question.
For example, my iMac doesn't have a battery (as far as I can tell), only my Magic Mouse does.

The title of this forum is Mac Desktops and Notebooks, my situation involved a MacBook Pro Notebook computer which does have a battery whether your computer has one or not. Additionally Mac Desktops and Notebooks is the ONLY available forum under the rubric of Hardware.

In this particular case the battery running down was a symptom/clue — not a cause. The cause was scrambled I/O from the hub which can and will effect any computer regardless of whether or not there is a battery in the computer. The solution required a full reset of a device, the TB3 Dock, that does not have a battery. If it had a battery the fix would nave been far more difficult requiring removal of the battery.

I don't understand your point. Perhaps this discussion would be better moved to FineTuneMac Feedback?

Thanks for clarifying that the macOS 10.14.4 update was a potential factor; I'll bet that confused you.

I've lamented the dearth of real troubleshooting-necessitating issues in the past few years more than once, because, as you've pointed out, the techniques tend to fade from memory and not be readily available when needed.

My only point is/was that the hardware in question should have been defined/described from the outset — as is consonant with FTM's philosophy and recommendations (and often demand) when describing problems. (I would have thought that, as a moderator, you would have been sensitive to such.)
Otherwise such commentary leaves one guessing as to what's being discussed. Hence my initial query.
Your latest response that "my situation involved a MacBook Pro Notebook computer" answers that question.
Enough said.

My troubleshooting technique:

Problems: 1. Adobe CS5.5 performance in High Sierra. 2. After installing a wireless mouse and USB wi-fi plug, my two CD drawers would open on cold boot.

Solution: "Google it". Somebody somewhere has had the problem and knows how to fix it.

More problematic was when my internet connection failed (new supplier) and the only way to contact the supplier was by, um, internet. The solution was to wait for three hours. I spend far too much time on the internet. I hardly knew what to do with myself...