webclient: remove 'Planning' label from wait indicator; add scroll-to-bottom button ...

- Waiting indicator now shows only a spinner (text was misleading — model
  doesn't always plan before responding)
- Add floating scroll-to-bottom button that appears when scrolled >200px
  from bottom, disappears when near bottom; smooth fade+slide transition;
  positioned bottom-right (under thumb on mobile)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>