When joining a new team, is it better to have the right soft skills and have to learn the hard skills of the job? Or vice versa?

To be a strong product manager, you will have to learn to balance your art in the science. That is your hard and soft skills. When you are new to a team, naturally you want to show your value and start to contribute right away. However you don't take the time to understand the dynamics of the existing team, build the right relationships, understand communication styles, you may set yourself up for failture even before you start. My recommendation would be to come in, get an understanding for the team and what their needs are. Build relationships, understand what skills are best used in the beginning.

I don't think it's black & white. There is a broader spectrum of colors here. Leverage your superpowers to shine and learn the skills that help you do your job better. What matters is delivering results that move the business forward. These results will be noticed, and the rest will organically follow.