[1.0] Connect run views and deduplicated per-run live output

The dashboard needs to show actual execution records, and streams keyed only by agent name can mix parallel runs or duplicate history when views reopen.

Scope

• Wire a run list and details to the authorized history API using Context.task_id/run identity.
• Show agent, status, input/output references, timing and permitted errors for the selected run.
• Key logs/stream output by run and merge history/live data with stable identities instead of appending duplicate history.

Acceptance criteria

• Two simultaneous runs of one agent remain distinguishable in details, logs and live output.
• Reopening a view or reloading the browser does not duplicate already-shown history.
• Empty historical coverage and loading failures are honest UI states; supported interactions are keyboard accessible.

Boundaries

Network reconnect reconciliation and lifecycle buttons have separate tickets that build on this view.

References

• Parent topic: #374.
• Implementation dependencies: #431, #443.
• src/flock/frontend/src/components/details/RunStatusTab.tsx
• src/flock/frontend/src/components/details/LiveOutputTab.tsx
• src/flock/frontend/src/store/streamStore.ts

Start with src/flock/frontend/src/components/details/RunStatusTab.tsx and LiveOutputTab.tsx, then trace how src/flock/frontend/src/store/streamStore.ts identifies streams and how the authorized history API is consumed. The work is done when run identity separates simultaneous runs, history and live output do not duplicate on reload or reopen, empty and failure states are honest, and supported interactions are keyboard accessible.