If I want my plugin to do $SUBJECT upon successfully saving form input, do I need to use messaging to set up a popup-only provider specific to my plugin, or is there a simpler way to just flash a brief message on the screen?
Normally, most Moodle forms accept HTTP POST data, process them (store in the database typically) and then redirect to a page that displays the success message with a continue button (continuing automatically after several seconds usually). Typical example is posting to a forum.
I know this is quite out-fashioned these days. There is no "on-next-screen notification API" I am aware of. However, if you are redirecting the user back to a page served by your plugin, you can easily implement such support yourself. I used something like that in the workshopallocation_random plugin.
One option is to call redirect(url, message) using the optional second message parameter. That causes a simple page to display briefly (3 seconds, by default) with the message, then redirecting automatically to the given URL.
Re: Displaying a simple "update successful!" message
If you don't like redirects (because you are allowed to ;) , you can store your messages on $SESSION or $USER and use $OUTPUT->notification() to print notifications using bootstrap classes.
Altough it is on the (much) older docs (https://docs.moodle.org/dev/Output_Components#notification) it seems to work pretty well.
Re: Displaying a simple "update successful!" message
$OUTPUT->notification() is nice. I'm going to start using that. (With redirects ).