Optimize model picker search rerenders

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What Changed

• Split the model picker search field into a small memoized ModelPickerSearchInput that owns the raw input value.
• Kept ModelPickerContent state normalized to the trimmed query used for filtering.
• Preserved Escape and Enter behavior while preventing whitespace-only input from invalidating the expensive picker/list subtree.

Why

React Doctor was run with pnpm dlx react-doctor@latest . --verbose --category performance --no-telemetry to identify performance/rerender concerns, then I manually profiled the model picker hot path with React Scan enabled. The baseline showed whitespace-only search input, which does not change visible results, still caused excessive model picker commits.

UI Changes

Before/after React Scan recordings were captured as Cursor artifacts:

• Before: before_model_picker_whitespace_rerenders.mp4 — five spaces in the search field increased ModelPicker profiler commits from 4 to 35.
• After: after_model_picker_whitespace_rerenders.mp4 — the same interaction finished at 9 commits, with only the local input work remaining.

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:

• vp check (passed; existing warnings reported outside this change)
• vp run typecheck (passed)

  

Note

Reduce rerenders in model picker search by extracting a memoized ModelPickerSearchInput component

• Extracts the search input UI and its event handling into a new memoized ModelPickerSearchInput component in ModelPickerContent.tsx, preventing the parent from rerendering on every keystroke.
• The new component maintains its own inputValue state and emits only trimmed values via onSearchQueryChange, so the parent ModelPickerContent updates searchQuery only when the trimmed value actually changes.
• Enter and Escape key handling is moved into the child component via callbacks (onEnterHighlightedModel, onEscape), and model selection logic is extracted into a reusable handleSearchEnterHighlightedModel handler in the parent.

^{Macroscope summarized 31520e0.}