feat: Add transcript text search to AI chat - #628

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@packages/ai-core/__tests__/ChatSearch.test.tsx`:
- Around line 66-71: The test mutates a module-scoped variable (latestSearch)
during render in SearchController which causes the lint error; instead stop
reassigning latestSearch during render by making latestSearch a React ref or
state held by the test and have SearchController assign into it inside a
useEffect (or expose the hook result via a callback prop) after mount; update
the test to declare latestSearch as a MutableRef (or provide a setter function)
and in SearchController call useChatSearch() then set ref.current (or call the
setter) inside useEffect so no module-scoped mutation happens during render
(references: latestSearch, SearchController, useChatSearch).

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@packages/ai-core/src/components/AnalysisResult.tsx`:
- Around line 375-385: The JSX for ReasoningBox is malformed and passing an
undeclared prop: remove the className prop from the ReasoningBox invocation
(since ReasoningBox props don’t include className) and fix the tag nesting so
HighlightedChatSearchText is a child of ReasoningBox and ReasoningBox is
properly closed (use <ReasoningBox key=... text={part.text} isRunning={...}>
...</ReasoningBox> with HighlightedChatSearchText as the inner element). Ensure
you keep the existing props (key, text, isRunning) and the
HighlightedChatSearchText props (blockId, text) unchanged.

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@packages/ai-core/src/components/AnalysisResult.tsx`:
- Around line 220-254: Generate search blocks only for the same parts that are
actually rendered: before the forEach over uiMessageParts, filter uiMessageParts
using the same predicate the render path uses (exclude any part whose index
appears in the suppressed indices collection used by rendering and exclude parts
with ids that start with "step-"), then map that filtered array through the
existing isTextPart/isReasoningPart/isToolPart/isDynamicToolPart logic (using
getToolName and processAnalysisAnswerContent as before) so searchBlockPrefix and
analysisResult.id remain, ensuring returned blocks match visible highlights.

  isSuccess: boolean;
  isError: boolean;
  toolCall: AgentToolCall;
  searchBlockId?: string;
}> = ({toolCallId, isPending, isSuccess, isError, toolCall, searchBlockId}) => {
  const showDetails = useShowToolCallDetails();
  const {getActivityLabel} = useToolRenderBehavior();
  const timing = useStoreWithAi((s) => s.ai.toolTimings[toolCallId]);

const Root: FC<RootProps> = ({ children, toolRenderBehavior }) => (
  <ToolRenderBehaviorProvider value={toolRenderBehavior ?? EMPTY_BEHAVIOR}>
    <SessionChatRuntimeProvider>
      <ChatSearchProvider>
        <SessionChatManager />
        {children}
      </ChatSearchProvider>
    </SessionChatRuntimeProvider>
  </ToolRenderBehaviorProvider>
);

const LocalAgentRoot: FC<LocalAgentChatRootProps> = ({
  children,
  toolRenderBehavior,
  ...props
}) => (
  <ToolRenderBehaviorProvider value={toolRenderBehavior ?? EMPTY_BEHAVIOR}>
    <LocalAgentChatRuntimeProvider {...props}>
      {children}
    </LocalAgentChatRuntimeProvider>
  </ToolRenderBehaviorProvider>
);