Phooey! Lost a post for the first time in ages.
I figured out what my Captcha problem is/was...
The only extensions I run are Wipr and Roadblock, both of which are content blockers, so I was turning them off from my menu bar.
But I remembered that Wipr just added a new component, Wipr Extra, which, as it has turned out, doesn't get turned off with the content blockers.
Disabling it, either with command-E or by unchecking it in my pref pane, enables me to log in to PayPal as usual. (I haven't needed it since I installed it, so I'll leave it unchecked and hold it in reserve against possible future need.)
(The problem I ran into at Small Dog appears to be unrelated.)