fix(web): sessions with live subagents or monitors no longer look stopped

[bk-agent-01]

Problem

A session that held an actionable plan went to the Plan Ready group even when its subagents or a monitor loop still ran. Plan Ready also hid the Working / Monitoring badge and the running glint. Thus the row looked stopped while the agent still worked. Plan Ready rows also had a violet pulsing row highlight that the user does not want.

Fix

• resolvePhaseSidebarPhase (shared in packages/client-runtime, so web and mobile both get it): background liveness (working / monitoring) now outranks a held plan. The row stays in Implementing or Planning. It goes to Plan Ready only after all work stops. A failure still files a held plan under Plan Ready.
• resolvePhaseSidebarWorkBadge no longer hides the Working / Monitoring badge for Plan Ready.
• New phaseSidebarIsAgentLive helper. The web row uses it for the solid PLAN badge, so a live row shows the outlined "Plan attached, agent still working" badge.
• Tree hoisting: a plan on a child that still works no longer pulls its parent into Plan Ready.
• Removed the violet pulsing row highlight for Plan Ready. These rows now use the default row surface. The PLAN badge and the group header still mark them.

Verification

• vp test run for PhaseGroupedSidebar.logic.test.ts, PhaseSidebarTree.logic.test.ts, RunningSessionGlint.logic.test.ts (151 passed) and client-runtime phaseSidebar*.test.ts (49 passed).
• vp run typecheck in apps/web and packages/client-runtime: clean.
• scripts/check-fork-markers.ts: passed.
• Not verified in a browser. Not shipped to expbkt3 first: the requester asked for a PR straight to bkmain. Merging deploys bkt3 and restarts its live sessions.
• No before/after screenshots: the cloud browser cannot reach dev-server-1 unattended.

Done by Claude Opus 5.5 in Claude Code (T3 Code).

🤖 Generated with Claude Code

[github-actions]

Thread transfer impact

✅ Thread transfer remains within every enforced ceiling.

ℹ️ No successful main baseline artifact is available yet. This run establishes the initial measurement.

Provider	Metric	Main baseline	This PR	Impact	PR ceiling
Codex	Total thread wire	—	13.7 KiB	—	15.1 KiB	✅
Codex	Thread snapshot wire	—	7.2 KiB	—	7.8 KiB	✅
Codex	Live turn WebSocket wire	—	6.5 KiB	—	7.8 KiB	✅
Codex	Live turn WebSocket decoded	—	56.3 KiB	—	66.4 KiB	✅
Codex	Live turn messages	—	9	—	21	✅
Claude	Total thread wire	—	13.7 KiB	—	15.1 KiB	✅
Claude	Thread snapshot wire	—	7.2 KiB	—	7.8 KiB	✅
Claude	Live turn WebSocket wire	—	6.5 KiB	—	7.8 KiB	✅
Claude	Live turn WebSocket decoded	—	57.1 KiB	—	66.4 KiB	✅
Claude	Live turn messages	—	9	—	21	✅

Baseline: unavailable · PR result: 8016a76 · Source CI: success

Scenario and decoded snapshot size

10 historical turns, 5 command tools per turn, 878.9 KiB retained MCP result per historical turn, and a 1.05 MiB retained result in the measured turn.

• Codex decoded thread snapshot: 114.6 KiB
• Claude decoded thread snapshot: 115.3 KiB

Updated in place by a trusted workflow. PR artifacts are strictly validated and never executed.