In this note the idea behind purpose is very linked with user scenarios, as they are a tool to help you identify purpose.
Design systems are made up of three main parts:
Don't just focus on the Elements - that alone creates a design system of good parts that don't work together. Importantly, keep the purpose in mind.
A good way to keep the purpose of your design system in mind is to:
Focusing on scenarios is a great way of making sure you're focusing on the purpose, and by relation, the interconnections to achieve that purpose.
Brad Frost's UI inventory groups by type - buttons, links, forms, etc. Alla Kholmatova's Purpose-Directed Inventory groups by purpose - discovery, learning, etc.
The latter is a tool better for finding patterns joined by a shared purpose. It helps find the differences between presentational differences vs semantic differences. Do they look the same and solve different problems, or the opposite? An audit like this helps you find opportunities for cohesion and consistency, and can act as a tool to reduce confusion.
Scenario-driven documentation is another potential area to focus on. Designers are often thinking in scenarios, so tailoring documentation for that helps drive adoption in a self-service way.
Scenarios also tie into variations. Create variations for needs. They should have a purpose. Don't create variations if they're achieving the same purpose, and don't tie into brand expression.
This is part of what makes design systems so hard - the interconnections and purpose mean that any component addition, update, etc. is tied to similar components in the area (interconnections), and the goal this component is trying to solve for the user (purpose).
https://www.smashingmagazine.com/2023/05/design-patterns-collaborate-design-system/