Task board split and crumbs: polish seen

Seen while testing Task 7179 on the live stack (/tasks, 1024px split with a task open; 448px). 1. The project crumb's System chip ("cto" is a system project) stays at full width when the crumb shrinks on the one-line trail, so the name drops to "c…" while the chip takes the room. Drop or shrink the chip before the name ellipsises. 2. In a 1024px split the board's row titles cut to ~25 characters ("Answer the open question o…") while the right pane keeps a wide empty gutter beside its tabs. Give the list more of the width, or let the pane's header row use it. 3. Opening a draft epic in the pane logs a 403 on GET /api/tasks/<id>/live-cast. A draft has no live cast; don't request it, or answer it without an error. 4. The dev console logs MUI/emotion's ":first-child is potentially unsafe" error twice on every /tasks load. Switch that selector to :first-of-type. Out of scope: the bulk bar, the Help launcher's lift, and the breadcrumb's title floor (Task 7179). Done means: - Each item shipped with a test, or declined with a stated reason. - Screenshots at 1024 and 448 showing each changed surface.

Shipped all 4 items with tests in PR #5865 (merged 34b3d72; deploy success). The System chip shrinks before the name, the pane header uses the right gutter, live-cast is asked only with the product (no 403), and the :first-child selectors are now named slots. Visual check at 1024/448 done. Follow-ups filed as draft 7219.