Use the empty space right of the breadcrumbs for the env's key facts: where it runs (multi-cluster only), PR, stack, template, cost and updated. Below it is a single row with the name, status, labels and actions. There's no separate facts band.
Details
The facts are right-aligned next to the global icons. They are listed by priority. When space runs out, whole chips drop off from the lowest priority up. They never wrap or get cut mid-word.
The breadcrumb's env crumb is capped at 220px because the full name is right below it.
The pinned top is about 160px: breadcrumbs with facts, the title row and tabs.
Trade-offs
The top bar is global navigation in every other page. Putting page data there is unusual, and it needs to look clearly different from nav, hence the grey chips.
On narrow screens most facts drop off, so they need a home elsewhere such as an ⓘ panel.