OK, I think I figured out what was going on. It is possible to to select text frames without having to repeatedly use the toolbar arrow icon,
but this will not work when you switch between spreads. For example if I am working on a spread composed of pages 62-63 and I need to go copy some content off a spread on pages 10-11,
the only way I can select a text frame on the new spread is by clicking on the arrow icon on the toolbar. Once this is done the keyboard shortcuts do work on the new spread.
Still, this is a lot better having to continually click on that arrow icon when working on the same spread, so I am going to mark this thread as "SOLVED". Thanks for helping me clear this up.

And if you know of a shortcut for selecting a text block immediately
after changing spreads in Scribus, do share. It will save lots of time for me because I need to do a lot of copying within a document.