Move search to the top of the conversation area, remove its visible heading, and use a white surface in the light theme. Keep the list independently scrollable and sidebar controls reachable in short windows. Standardize footer divider spacing to 16px on both sides and update layout tests and design guidance.
Validation: 307 focused tests, typecheck, targeted ESLint, and four Electron layout scenarios passed.
Release note: Conversation search now sits above the conversation list in a distinct themed area, with consistent divider spacing and improved short-window scrolling.
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