Conversations are organized with search, history, or folders

When every session starts from an empty chat and old conversations either disappear or live in one flat scroll-list, users stop building on prior work. The conversation archive is the product's long-term memory and compounding value; without search, folders, or at minimum date grouping, that archive becomes write-only — users keep typing into it but never read back. Competitors with proper history UX retain users on the strength of accumulated context alone.

Ship a sidebar that lists conversations in reverse chronological order grouped by Today / Yesterday / Last 7 days / Older, with a top-of-sidebar search input hitting /api/conversations/search?q=. Auto-title conversations from the first user message. Implement the sidebar at src/components/chat/conversation-sidebar.tsx.

<Input placeholder="Search conversations..." onChange={e => setQuery(e.target.value)} />