Do you split your Design System?

Hey! How do you split your design system when you have a website and a product? Do you have two different UI kits with shared foundations (color, icons, typography, etc.), or do you have two different design systems, which live their separate lives? Or maybe you don't split it at all?

In my company, we currently have two storybooks for a website and for a product, because we used different technologies to build those. But we had just one DS file in Figma. Now I have time and resources to make it properly, so I'm thinking, should I split the system in Figma into two different ones, and keep them synced just with the related storybook?

I can't find examples of how other companies are doing this, but it looks like all the famous DS like Polaris, Primer, Pajamas are just for products, and they probably have another system or UI Kit for their websites.

Anyway, I'd be happy to hear your thoughts on splitting Product and Website, or keeping them together.