JP C. answered 10/16/19
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This is an excellent observation! I would argue that the word "secondary" should be seen as "temporary" without the express intent of modulation.
As for the function of these mediants and submediants, (depending on the context of course!) they could be used as either substitutions of V and ii respectively depending on the context or an elongation of the secondary harmony as a "temporary key".
Very interesting question! Please update us on any findings! :-)