According the the "Inkscape Beginners' Guide" if I hold the control (ctrl) key down when drawing a rectangle I will actually draw a square.  Ditto for the  Ellipse/Arc tool.  With both as I hold the control key and the left mouse button and pull the mouse depending on the exact path I move the mouse I may get a square then suddenly it changes to a rectangle.  If I continue to move the mouse I will then get a square again.  Circles have the same behavior.

Why is this happening?

I am running a newly installed Inkscape 1.3.2 on Windows 10 Pro using the MSI installer from inkscape.org website; with Dell hardware with all Microsoft updates applied.

Well, it's not a bug, it's a feature :) If you look at the bottom of your window after you started dragging, you will see a little text telling you what modifiers (alt, shift, ctrl) to use with the tool and what they do (see capture below) :
  - "with Ctrl to make square, integer-ratio, or golden-ratio rectangle".

The same goes with ellipses. So if you want a perfect square, you have to keep the cursor near the 45° diagonal while dragging.

Thank You.

A feature that is not documented in the beginners guide.  I am new to all of this, is there a way to send a suggestion the the beginners guide author(s) that some kind of note needs to be included so that future learners are not confused?

If you're talking about this manual:
https://inkscape-manuals.readthedocs.io/en/latest/

...then yes there is way to get it improved (this is explained on the first page of the manual). You can open an issue here:
https://gitlab.com/inkscape/inkscape-docs/manuals/-/issues