More experimenting with Mobile Sync reveals the following: (Specs for iOS and Accordance are in the OP)
Each category of the iPhone App Library has texts/tools present before syncing.
On the macOS side I observe the following screen:
If I stop the sync, the iPhone side will be unchanged. If I start the sync—all texts on the iPhone are removed unless a text is chosen for install.
I first noticed this when I chose to update only and add no additional texts and found that the Texts folder of the library was empty on the iPhone.
I never really paid much attention to the folder titles before, but I see that the two sides do not match. For example the iPhone Library has devotionals, but the mac side does not.
A real puzzle: On the mac side Tools and Notes are shown to sync nothing (as Texts), but the sync process did not disturb the tools in these sections of the iPhone App Library.
A puzzle indeed!