Agentic UI: Fix chat opening at the top after a cold start

[shaunandrews]

Related issues

• None

How AI was used in this PR

• Claude Code diagnosed the regression, wrote the fix and the regression test; diff reviewed by hand.

Proposed Changes

• On a cold start, Studio opened the most recent chat scrolled to the top, and the scroll-to-latest button never appeared, even after scrolling up.
• Cause: the session is served from the persisted query cache before the AI-credits quota check resolves, so the conversation scroller mounts in a later render than the session data. The scroll effects ran once against a not-yet-mounted scroller and never re-ran. Regression from the quota gate in Surface Studio Code payment-method requirement before the first prompt #4422 landing on top of the autoscroll pause in Agentic UI: pause chat autoscroll while reading earlier messages #4575.
• The scroll effects now key off the scroller itself, so the chat opens at the latest message and the button works regardless of which query resolves first. The same path covers the payment-method gate → chat transition.

Testing Instructions

1. Quit Studio fully and relaunch so the quota query is cold.
2. The most recent chat opens scrolled to the latest message.
3. Scroll up: the scroll-to-latest button appears. Click it to return to the bottom.
4. Switch sessions and repeat.
5. npm test -- apps/ui/src/ui-classic/components/session-view/index.test.tsx — the new cold-start case fails on trunk and passes here.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

🤖 Generated with Claude Code

[wpmobilebot]

📊 Performance Test Results

Comparing 3a0232e vs trunk

app-size

Metric	trunk	3a0232e	Diff	Change
App Size (Mac)	1456.84 MB	1456.84 MB	0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	3a0232e	Diff	Change
load	1192 ms	1186 ms	6 ms	⚪ 0.0%

site-startup

Metric	trunk	3a0232e	Diff	Change
siteCreation	7523 ms	7589 ms	+66 ms	🔴 0.9%
siteStartup	3373 ms	3370 ms	3 ms	⚪ 0.0%

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Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change (<50ms diff)