Conversation title is auto-generated or set on creation

A history sidebar full of rows labeled "New conversation" or UUIDs is functionally useless — users cannot find anything, so they start a new chat every time instead of continuing old ones, which defeats the point of persistence entirely. Auto-generated titles turn the archive from a dead dump into a searchable, scannable record of prior work, and they cost roughly a fraction of a cent per conversation when generated by a cheap model like gpt-4o-mini or claude-haiku.

After the first assistant response lands, fire a background call to a cheap model asking for a six-word title summarizing the opening exchange. Persist via UPDATE conversations SET title = $1 WHERE id = $2. Fall back to the first fifty characters of the user's opening message if the generation fails. Implement in src/lib/ai/generate-title.ts.

const { text } = await generateText({ model: openai('gpt-4o-mini'), prompt: `Six-word title for: "${firstMessage.slice(0, 200)}"` })
await updateConversationTitle(id, text.trim())