How do you approach working with cross-functional teams to ensure work is done on the highest impact initiatives?

Let me answer this more broadly. For any organization, it's important to have alignment across the different functions, including Product Management, Operations, Design, Engineering, and Data Science. You wanted to have a small leadership team that works very closely with shared KPI's and goals. Then the question is more around what projects to work upon to meet the KPIs. This is typically done through a lightweight prioritization framework. There are many industry standards for sprint management and prioritization. The key is to ensure there is the right leadership team with aligned priorities.  

On a daily basis, product manager's job is to bring clarity and alignment among teams. As a consequence, working with cross functional teams is part of the job.

I wouldn't have one answer on how to do so, as it really depends on the situation. There are lots of different frameworks that can work depending on the situation, and the best PMs know which ones to use in which situation.

But at the end of the day, what really matters and what makes a difference is the relationships you have with other teams. So as a PM, I would advise to spend time on creating relationships with other teams, rather than focusing on the process.