We designed a process that included component review cycles and signoff. However, instead of forcing a component to get design system signoff, we allowed it to move forward to production before worrying about making it a Core or Shared component. This not only let product teams move faster, but also gave us time to see how a component would perform before making it a Core or Shared component.
Three levels of components helped us communicate clearly about who owned a component, how (or if) it could be changed, and why it existed. This also created a clear process and review cycle for feature components to become shared components.
In our Feature Team (Store Systems), I was able to help a product quickly design and deliver a date picker component using established core components, and use the delivered design to inform a date picker component that would be shared among other feature teams. We were able to keep the project on track because we weren't stuck on designing a shared component first, but focused on designing for the need at hand (a feature component), then focusing on the longer task of designing a component that could be shared across feature teams.