fix(ui): make session activity state truthful

[wolfiesch]

Summary

• distinguish idle, stopped, and unknown session lifecycle states
• show a persistent working heartbeat with elapsed time for confirmed live work
• clarify saved-step observer updates and diagnose mixed OMP installations
• allow enough time for a healthy macOS OMP cold-start probe

Verification

• pnpm check
• pnpm test
• pnpm build:web
• focused web and desktop runtime tests
• local dark-mode UI screenshot at 1512x982
• live t4-doctor run detects the mixed OMP setup while the default appserver remains healthy

[chatgpt-codex-connector]

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