Reduce model picker rerenders for whitespace search input

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What Changed

• Split the model picker search box into a small memoized input component that owns raw keystroke state.
• Added normalizeModelPickerSearchQuery so the expensive picker/list only receives semantic query changes (trimmed, lowercased, whitespace-collapsed).
• Added a focused unit test covering whitespace normalization.

Why

react-doctor/manual inspection pointed at hot React surfaces in the chat/model-picker area. React Scan showed whitespace-only typing in the model picker search was still invalidating the picker/list even though the effective search query did not change. Keeping raw input state local avoids recomputing/filtering/rerendering the model list for no-op whitespace edits while preserving normal search behavior.

UI Changes

React Scan recordings captured with the temporary fixture around the real ModelPickerContent component:

• Before: react_scan_model_picker_before_whitespace_counter.mp4 — typing five spaces shows React Scan rerender highlights over the picker/list rows.
• After: react_scan_model_picker_after_whitespace_counter.mp4 — the same five-space input no longer highlights the visible model rows; the search field still accepts the raw spaces locally.

Checklist

• This PR is small and focused
• I explained what changed and why
• I included before/after screenshots for any UI changes
• I included a video for animation/interaction changes

Validation:

• corepack pnpm --filter @t3tools/web exec vp test run --passWithNoTests --project unit src/components/chat/modelPickerSearch.test.ts
• NODE_OPTIONS="--experimental-strip-types" corepack pnpm exec vp check
• corepack pnpm exec vp run typecheck

  

Note

Reduce model picker rerenders by normalizing whitespace in search input

• Adds normalizeModelPickerSearchQuery in modelPickerSearch.ts to lowercase and collapse consecutive whitespace to a single space.
• Extracts a memoized ModelPickerSearchInput component in ModelPickerContent.tsx that holds raw input state internally and only calls onNormalizedQueryChange when the normalized value actually changes.
• Filtering and ranking in ModelPickerContent now use the normalized query, so purely whitespace differences in the input no longer trigger rerenders or recompute the model list.

^{Macroscope summarized 602ee51.}