Right now, the component is interesting, but it unfortunately lacks some important elements to make it fully usable:
It would be useful if it could support a badge (like the product page does in the admin). It is needed for all objects that have an active/draft status.
Not all pages are meant to be full-width. For instance, in Shopify admin the product edit page (in overall, most edit page) are easier to use when they are not full width. In the Shopify admin, the title bar automatically adjusts. Maybe the width could adapt automatically when inserted into a component that is not fullWidth.
Shopify admin uses tertiary button, but the ui-title-bar does not support them, hence causing inconsistent design.
Shopify seems to use an icon for breadcrumb, but this is not supported by the component. The problem is that the does not apparently supports the new components, which leads a strange experience (I would have expected ui-title-bar to accept s-button, s-icon,… but it does not).