How do you show Product Marketing's impact on metrics that are shared with another function?

What I would recommend is having very transparent conversations with key stakeholders and collaborators across the other departments with whom you might be sharing a KPI. I used pipeline contribution as an example earlier, so I'll use product adoption as a KPI you might share with the product team.

In this case, instead of thinking about product adoption as a split metric, or metric that you need to attribute some of to PMM and some to PM. It really should be a shared metric for both. There's a significant amount of work that the product team will have done to ship the product, and there's a significant amount of work required of the PMM to build the right plan to take the product to market, so "credit" should be shared equally as you start to see product adoption increase.

First, you have to ensure you have alignment on what KPIs you are driving towards, and how you're tracking them. This starts with alignment conversations across marketing, product, sales, customer success early and discussing not only what their goals are, but how they plan to measure them as well. From there, establishing shared dashboards, recurring meetings where you discuss progress towards goal (and any changes along the way), and a post-mortem analysis of how it went and what could have been done better.