fix(ui): prevent tool status blank frame

[Hona]

Summary

• keep the perf optimization that only mounts both tool status labels during animation
• flip data-active synchronously, then defer the target-width measurement to the next frame so the incoming label is mounted/measurable
• preserve the measured-width transition for the Exploring → Explored status title without the blank/drop frame

Chrome trace benchmark

Setup:

• 1000 timeline status rows on one page
• Chrome trace via CDP
• 4x CPU slowdown
• 5 traced runs per variant
• same isolated real-component harness/CSS/theme across variants

Variant	Visual	Runs	Main avg	Main median	Max task avg	Max task range	Long tasks avg	Script avg	Style/Layout avg	Paint/Composite avg
Current dev	❌ blank/drop frame	5	82488ms	81526ms	2695ms	2327.9–2838.0ms	198.0	1380ms	5447ms	34522ms
Old correct, pre-perf revert	✅ correct	5	77271ms	74614ms	8700ms	7820.4–9301.9ms	174.8	5125ms	5087ms	28365ms
Fixed PR	✅ correct	5	47638ms	30071ms	8029ms	7913.3–8194.8ms	59.6	6194ms	4227ms	16426ms

Readout:

• Fixed PR restores the visual transition without returning to the old always-mounted behavior.
• Versus old visual-correct behavior: lower main-thread trace time, fewer long tasks, slightly lower max task, lower style/layout, and lower paint/composite.
• Versus current broken dev: fixed has a higher max task because it performs the real target-width measurement/animation work, but lower total main-thread time and fewer long tasks while preserving correctness.

Validation

• bun typecheck from packages/session-ui
• push hook full turbo typecheck passed
• recorded isolated real-component harness video for Exploring → Explored after the fix

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