Keep the phone controls on screen inside in-app browsers

The root height fell back to nothing where dvh is unsupported, so the
bottom-anchored add button and action bar sat far below the fold. Use a
vh fallback plus the measured innerHeight, add viewport-fit=cover, lift the
bottom controls above the safe area, and give the phone note a gap under
the header pill.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>