How should customer success split product adoption KPI’s with Product and Sales?

It should NOT!

Adoption is the job of everyone in the company and the ultimate owners of the adoption KPIs would be the business owners (CEO, BU leaders).

We succeed together and we fail together. If a customer isn't successful it doesn't really make a difference if your team/department has done the job in an excellent way. We still have failed as an organization on our purpose and that is what everyone should be focused on.

Adoption KPIs are in general lagging indicators, which make it less useful and interesting to split them. What you should strive instead is to analyze what are the key capabilities and key factors driving adoption for your customers and identify leading indicators for each of those. This way, you can see where in the organization there is more work required to level up and increase our ability to influence the adoption of customers.

Those leading indicators should cover the full journey of the customer as adoption starts even before the sale is made.

For example: Sales and Sales Engineering/Solution Architecture are the first to create a baseline for adoption. They do so through the expectations created in the sales cycle about the value of the product - available use cases, measurable success from other customers, capabilities that can be created towards customer's ambitions and strategic objectives. Customer Success takes over those expectations and promises in order to further elaborate them and convert them to shared and committed action plans including everyone in the organization as well as the customer stakeholders who drive the adoption on their side.

Think about what key leading indicators point to opportunities/deals which grow faster and better in terms of adoption and use those for defining the different functions' OKRs.