Your remark that regardless of dye something physically exists is real -- suggests that your conditions for real are limited to that which is physical.

But if you say hyperreal is not real then you would also denying that our sense of who we are, constructed in media, is "real" or the suburbia as a created community, born out of the culture of propaganda (circa 1940s-1950s) has a "real" effect on home prices (people having a preference to live in suburbia), and so on (as such preferences have no physical existence).

In a deep way hyperreality is an extension of the realness of language via media and culture... to deny that language is real in any profound sense, would also entail denying that your name or my name is also real in that sense (regardless of the reality of our physical existence)... that would also be denying everything that "exists" in language or culture.... ie, denying there are "colors". Certainly there is a wavelength for a given sensory impression of blue, and people who have functional eyes can agree that two things are the same shade but as far as what is a color -- that isn't physical... in some language/cultures might say this is only blue, others might say it is a different color entirely (green, or in russian, denying that there is a color blue, as that spectrum is split into multiple colors)

So idk if that is what you mean to include (I suspect not) but to say that things are only real if there is a physical existence (hyperreal is not based on the physical) is not how we humans generally consider our experience.