I have been noticing more and more of these cropping up. There are several spots in my garden (some under a plant, some not) where a dim ball of swirling, pulsating, rainbow-colored lights are just sitting there on the ground. They are completely non-interactive, and they are completely independent of what type of plant is nearby. What in the world are they?

The first thing that comes to my mind is that this sounds exactly like the effect of the Collection Helper. Do you have this activated by any chance?

edit: Could you post a screenshot?

Not the collection helper. That is a white sparkly effect and is visible from the aerial view. This is just on the ground, in my garden, on my lot.

Sorry I was going to add an image but I cant get into my usual image sharing account right now, and I was on the way out the door. Here is a temporary one:

https://ibb.co/igvEQa

In that image, the orbs happen to be next to some Life Fruit plants, but they appear on or next to pretty much anything, but only in my garden. They usually hang around a couple days, then disappear.

This is the visual effect of life fruit and it probably ended up there because you either harvested some or deleted a life fruit plant while it carried fruit.
As you noted the effect will disappear after a while or when you save and reload the game.
As to what causes it? No idea, but do you use ErrorTrap? I am asking because I have found that when I have ErrorTrap in my games that some visual effects appear to linger for longer in my game than they should.

I use ET now, but this effect occurred long before I started using it.
I HAVE been planting alot more LFP recently as I ramp up my nectaring, and noticed an uptick in the occurrences. I thought at first it might be related to the LFP as well, but it appears in locations where I did not have any LFP planted -- like across the garden next to other plants. Though if LFP isn't the only plant that leaves a "residue" when deleted, that may be it after all (I also noticed it frequently near my Plasma Fruit plots, but other plants as well).

I'm almost totally sure it's because of life fruit. I've seen the same thing happening and it never happens before my sims start planting life fruit plants.