This tension is why I refer to myself as a product engineer. Teams where non-technical product managers (ie. your "product team") become feature factories that eventually drown in their own tech debt. Teams where navel-gazing engineering managers (ie. your "engineering team") have too much power end up with premature platformization, and beautiful architecture diagrams while user needs go unmet.

The key is to understand that computers exist to serve human needs, and the less code / UI / hoops to solve a problem the better, and to think end-to-end. If you are able to do that, most systems built by committee have a lot of low-hanging fruit that can be improved without much sacrifice. In practice, political realities and operational concerns may come in the way, but I firmly believe this is the only way to successfully operate as an engineer, and it will only become more important in the age of AI.