I know it sounds obvious, but it's important to have an open and early conversation about decision-making to avoid this becoming a blocker further down the line. You can use a RACI or DACI model to guide these conversations and achieve calarity about who owns a decision. The added benefit of models such as RACI and DACI is that they will help clarify overall responsibilities when working on a product or project.
https://monday.com/blog/project-management/raci-model/
https://www.productplan.com/glossary/daci/
Ultimately Product Management is about people. I do approach stakeholders differently, but it’s based on who they are, rather their role. Some stakeholders like to be consulted ahead of time, some prefer being briefed in bigger forums where they can gauge the reactions of others. Some like structured approaches, others react to the anecdotal evidence. Some may have specific trigger points on specific topics.
Part of my role is to understand those differences and be able to navigate through them.
No, the foundations of stakeholder management are the same for me, irrespective of the discipline and expertise involved. Like I mentioned in one of my earlier answers: listening and developing empathy are key, as well as involving stakeholders early and often in the product (development) lifecycle.
I measure the success in my role based on the measurable value that my team and I deliver to customers, which in turns translates into business results. Example metrics are (increasing) conversion rate or (reducing) response time to end-users.
I wouldn't say the KPIs themselves have evolved dramatically. The leading and lagging indicators that I've been accountable for thus far have varied based on the products (e.g. B2B vs B2C metrics). As I've grown within my role, I've become accountable for a portfolio of products, as opposed to the success metrics for a single product.