Almost every thermoplastic is recyclable easily, though not necessarily profitably (because the new materials are so cheap).
Recycling that PET bottle into a different usable object would involve cleaning it, cutting it into a shape appropriate for your chosen remanufacturing process (filament or flakes), heating it to melted but not too hot, then forming (fdm, molding, etc.).
My guess would be that getting a durable graphic printed on PET is more difficult since we don’t see that, and adhesive or wrapped labels are almost certainly more expensive than printing would be if it were easy.
Edit to add: I agree that more responsibility needs to be on the manufacturer, but don’t buy into the misinformation that plastic can’t be recycled. Make it more expensive to use new plastic than recycled material.