Dashboard: segment-level progress indicators for multi-segment tasks

[HenryLach]

Problem

During multi-segment task execution, the dashboard gives no meaningful feedback for non-final segments. The .DONE suppression (TP-145) correctly prevents premature completion marking, but the side effect is that the dashboard shows the lane as running with no progress signal — you can't tell if the segment is progressing, completed-but-suppressed, or stuck.

This is especially noticeable in wave 2+ where all tasks may be on segment 1 of 2 — the entire wave looks like it's doing nothing.

Desired behavior

• Show which segment is currently executing (e.g., segment 1/3 · shared-libs)
• Show segment completion status (e.g., ✅ segment 1 · ⏳ segment 2 · ⬚ segment 3)
• Progress bar should reflect current segment's checkpoint progress, not just overall task
• When a non-final segment completes, show a visual indicator that it finished (even though .DONE is suppressed)

Context

• .DONE suppression for non-final segments is correct and must stay (TP-145)
• Lane snapshots already include segmentId — the data is available
• The segment frontier is tracked in batch state
• Related: worker checkpoint compliance is non-deterministic (RULE chore(deps): bump actions/checkout from 4 to 6 #1 not always followed), so segment-level indicators add a reliable platform-controlled progress signal independent of worker behavior

[HenryLach]

Triage update (2026-05-10): still relevant. Folded into TP-197 — dashboard segment-level progress indicators. Kept separate from the multi-segment engine hardening work (TP-196) because this is a pure dashboard UX concern in dashboard/public/ — different file domain, different validation approach (manual visual verification vs unit-test-driven). Will auto-close when the TP-197 PR merges.