Should aspiring hard-tech founders join a problem-first or technology-first PhD lab? (I will not promote)

I'm an engineering undergrad considering pursuing a PhD with the long-term goal of founding a hard-tech startup. I’m undecided about the specific area and have only a vague sense of what interests me (some areas that currently interest me are industrial decarbonization, mining / mineral processing, and advanced materials). However, I'm unsure which type of PhD lab would be better: a problem-first lab (e.g., like Yet-Ming Chiang's lab at MIT) or a technology-first lab (e.g., a typical academic lab that focuses on novel science without a predetermined application, and where commercialization happens largely by chance -- when a technology happens to have a valuable market application). I've looked at advice online from successful hard-tech entrepreneurs, but found conflicting answers. Some say to work backwards from a problem, while others argue that problem-first approaches often fail because it is difficult to force a scientific breakthrough around a predetermined problem.. Instead, they argue that most hard-tech companies are only founded because somebody made a scientific breakthrough and realized afterwards that there might be a commercial application. With that in mind, does anybody have any advice on which type of PhD lab to join?