~anthropic/claude-sonnet-latest → B (6:4)

Side B fixes a real, impactful bug (hardcoded staging/production hostnames breaking OAuth callbacks and redirects on custom hosts) by centralizing base-URL logic in a single util function and adopting HOSTNAME/window.location.origin, touching multiple real production files with clear lasting value. Side A improves test coverage and a display-path fix, which is useful but narrower in scope and mostly test churn plus a small correctness fix in one file.