If I recall correctly, my father said this baseboard electrical outlet would have been used for a vacuum cleaner, which had a screw-in light bulb type "plug" rather than a two-prong plug. Does that sound right?

I think that is right. I believe before the plug cap, they did use a screw in Edison base like we see on a light bulb today. That goes way back tho. Pretty hard to make TR I suppose, especially at baseboard height.
Keep an eye in the baby

I am actually surprised that the Edison base socket has lasted this long in this safety conscious world we live in now. I guess there is just too much installed hardware out there for a change.

Here's a picture of the matching plug:
https://stevenjohnson.com/stereoview/images/edison-plug.jpg

An older one:
https://stevenjohnson.com/stereoview/images/radio-junior01.jpg

Thanks for the confirmation and photos. Identification as an "Edison" plug led me to Museum of Plugs and Sockets which has some additional information.