At phone widths the header overflows: the guest trial pill pushes New chat into a clipped wrap and pushes Sign in fully off-screen, so a mobile guest cannot sign in. The provider select and Refresh reach button misalign, and the composer can sit below the fold.
Fix: move the free-message counter out of the header into the status row as small muted text (less prominent, per feedback), let the header fit phones, put select+refresh on one grid row on mobile, and pin the chat column to the viewport height so the composer stays visible and messages scroll internally.