I attempted to find terms like PET packaging and PET recycling in COCA, BNC, and so forth, but they are rare all around, and the results are not informative. I could not find an interface to Google NGrams that allows comparisons across corpora.
To venture from personal experience then, PET or PETE as a type of plastic would not be widely understood in North America outside of industry (and people who would consider themselves to be environmental activists). Reference to a PET bottle is likely to be interpreted as some sort of water bottle for a pet dog or cat, or as the next generation of pet rock— or would simply generate a blank stare.
Canadian and American consumers know most synthetic materials better by their trade names: nylon, not polyamide; Styrofoam, not polystyrene; Lucite, not PMMA. There are a handful of exceptions: PVC (polyvinyl chloride), and to a far lesser extent CPVC and PEX, commonly used in household plumbing; BPA (Bisphenol-A), known because of recent health concerns about its use in water bottles and food packaging (or perhaps more accurately, the heavy "BPA-free" marketing campaign subsequently waged by manufacturers); and PTFE, similarly from articles about health concerns relating to the material far better known as Teflon.
Secondly, although this is merely a theory, the recycling label may have contributed to PET / PETE being more widely understood in various parts of Europe and East Asia than here. With land and energy so cheap in North America, and because the lower population densities make it more expensive to do household collections, consumers never recycled much until the late 1980s, when the saga of "the garbage barge" became national news. Even then, rare was the community that attempted to recycle plastics. The numbering system was a response to the difficulty consumers had in distinguishing between a dozen different materials all generically known as plastic.
While there is much greater uptake of recycling nowadays, the modern practice is single stream; everything goes into the same bin. Many communities went from no plastic recycling at all directly to single stream. So, there has never been a reason for the average American or Canadian to pay attention to the mysterious plastic recycling codes, and we have never internalized HDPE or PP or PET as kinds of materials.