I simply had not seen the message in Dashboard Home telling me to complete the WP Members update (I’m trying to convince myself that it’s something new?)
Yes, that is new. And thanks for noting that cleared your issue because upon review, I do see that is likely the issue for the OP’s problem as well.
The plugin received a new component for finalizing installs and updates. This is primarily because over time, it has become increasingly difficult to efficiently handle the necessary update process when a user updates through an asynchronous process (such as clicking “update” in the plugin list where you get the spinning indicator).
Obviously, with anything new, there are new things that come up and the possibility for bugs occurs. Unfortunately, not all of those become apparent until after the fact. That is the case here. Following your additional info, and looking at the generated message, the form lacks a closing tag, which is a bug. So if it is left in place (i.e. ignored), then it will affect the other forms on that page as well.
As you noted, the simple solution is to clear the message by completing the action. Once the install or upgrade is finalized, the notification goes away and there is no form conflict remaining.
There will be a bug fix for this in whatever the next release is.