fix(chat): make the transcript follow the answer as one scroll model

[mrsibe]

What does this PR do?

Reworks the chat transcript's auto-scroll into a single follow model:
follow only while the reader is near the bottom, stop the moment they scroll
up, reserve the composer's real height, and offer one icon-only back-to-bottom
control.

Why?

Three reported symptoms share one cause:

• Streaming dragged the view back down even after the reader scrolled up to
  re-read a passage.
• "Back to bottom" landed with the last line still behind the floating
  composer, because it scrolled to an anchor and the composer's height was a
  hardcoded pb-32 that a growing scope row or a multi-line question outpaced.
• Height that arrived without a new message (Markdown reflow, code
  highlighting, images, an opened source disclosure) did not keep the follow
  alive.

What changed?

• Follow is decided by scrollHeight - scrollTop - clientHeight against a 48px
  threshold, clamped at zero for sub-pixel layout, instead of
  scrollTop + clientHeight === scrollHeight.
• A ResizeObserver on the transcript drives the follow from content height,
  so streaming and reflow both keep the end in view — only while pinned.
• scrollToBottom targets the viewport's true bottom
  (scrollTo({ top: scrollHeight })), not an anchor's scrollIntoView.
• ProcessPanel measures the composer and publishes --composer-reserve; the
  transcript's padding-bottom, the scroll fade height and the back-to-bottom
  control's offset all read that value.
• The back-to-bottom control is a circular, icon-only ↓ centred above the
  composer (32×32, tooltip "Back to bottom" / "回到底部"). Smooth for a
  deliberate jump; instant while an answer streams or under
  prefers-reduced-motion. A programmatic lock keeps the animation from
  unfollowing part-way, and wheel/touch/keyboard input cancels it.
• The transcript remounts per session, so a conversation always opens at its
  end.
• The scroll arithmetic lives in chat/stickToBottom.ts with
  test/stickToBottom.test.ts; DESIGN.md describes the new model.

How was this tested?

• npm run typecheck — passes
• npm test — 428 pass (incl. 11 new stickToBottom cases: threshold
  boundary, fractional pixels, negative clamp)
• npm run build — passes
• npm run check:design — no violations
• npm run lint — no findings in the changed files (existing any warnings
  unchanged)

Screenshots / recordings

Required for meaningful UI/UX changes. Not attached — no running desktop
session was available. The reviewer should confirm in npm run dev:
the ↓ position above single-line / multi-line / scope-expanded composers, the
smooth jump, and that the last line stays clear of the input.

Before	After

Checklist

• I have reviewed my own changes.
• npm run typecheck passes.
• npm run build passes.
• I have tested the affected user workflow.
• I have not included unrelated changes.
• I have updated documentation when necessary.

Desktop / build changes

• Not applicable