feat(results): add Refine flow, improved result states, and weekly funnel analytics

[chake111]

Motivation

• Provide a Refine entry on the results page so users can submit a follow-up query while preserving current filter/sort context.
• Improve UX for three key result states (loading, empty results, and no-match-under-filter) to reduce user confusion and surface appropriate CTAs.
• Add a small internal analytics surface to track a core search→converge→convert funnel and enable 1–2 quick experiments driven by the largest drop-off.

Description

• Add a Refine input and submit flow in the toolbar and results list and wire its handler in ui/components/results/results-toolbar.tsx and ui/components/results/results-list.tsx, keeping existing filter/sort context on submit.
• Extend useSearchFlow in ui/hooks/use-search-flow.ts to emit a requestId on each search and return it to callers so tracking events can be correlated with a single search request.
• Expand tracking helpers and server handling: update ui/lib/track.ts to include optional metadata on search and always forward metadata, and update ui/app/api/track/route.ts to persist search metadata; add track calls from results/home pages to include request_id, query, locale, and action context.
• Add a new internal funnel API GET /api/track/funnel implemented at ui/app/api/track/funnel/route.ts that returns stage totals, daily buckets, adjacent drop-off rates, and the largest drop-off node for the requested window.
• Improve result UI states by rendering dedicated loading, empty, and no-match messages and add i18n strings in ui/messages/en.json and ui/messages/zh.json.
• Add documentation docs/funnel-dashboard-and-experiments.md describing funnel stages, the one-week dashboard API, and two small-step experiment templates triggered by the biggest drop-off.

Testing

• Ran TypeScript checks with cd ui && npm run typecheck, which completed successfully.
• Ran cd ui && npm run lint, which failed due to missing ESLint flat config in the repo (environment/repo config issue rather than code type errors).
• No UI/browser screenshot tests were executed in this environment; server-side code paths were exercised by tsc type checking.

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Codex Task

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Project	Deployment	Actions	Updated (UTC)
ai-tool-picker	Ready	Preview, Comment	Apr 20, 2026 1:03pm