For those who are interested, I discovered the problem with my scheduled tasks (but not the weird refusal of Google’s search engines to crawl the site for indexing).
I’m probably going to make a hash of the explanation. That said…
One of the things that was getting progressively worse was more scheduled tasks began to fail. These are backend tasks that your average person doesn’t look at, but makes your site play nicely with other folks (for instance, the Jetpack plugin if you aren’t hosted by WordPress.com). Because you are potentially in the wild west on different hosts, there is a “Site Health” monitor. This monitor made my site look sickly because it wasn’t doing these background tasks anymore. This is what I usually see (without the “one thing”, but that is intentional).

But the past few days, I saw a sickly yellow and multiple tasks were suddenly not triggering in the background. No matter how I approached the problem, I couldn’t get it fixed. And then, this afternoon, the unperformed tasks grew…
I retried a few solutions, to no avail.
And then I did what I should have done when I first noticed the problem… I deactivated newly-updated plug-ins: one for site speed and optimization, another for stats, and my favorite whipping boy, Jetpack.
Can you guess which of the three made the sickly color go away?
[tension mounts]
No. Not stats.
[tension continues to mount]
No. Not Jetpack.
The very popular and nearly ubiquitous Litespeed Cache plugin was the culprit. Installed to increase speed and performance, it broke my site when I updated it. I rolled back to the previous version of the plugin and now… everything is back to behaving as expected. All greens/good.
The plugin meant to improve my site was actively borking my site.
Oh, for the love of…
So if you’re seeing something similar, be sure to try deactivating and rolling back the Litespeed plugin (cache is extremely useful and improves tons of things when it isn’t broken).

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