The add-to-cart Server Action should revalidate the /cart to refetch data from the database (e.g. showing the new items added to the cart) without a full page load (just using the Link component). The revalidatePath function seems to work with mutations on the same page, however, doesn't seem to cause a revalidation on other pages (in this case the cart page).
Current temporary work around - using <a> tags for linking to cart page in header and toast notifications, but this is far from ideal.