Migrate Langfuse integration from langfuse-vercel to JS SDK v5

[hassiebp]

Hi Sourcebot team 👋 — I'm Hassieb from the Langfuse team.

Sourcebot has two separate v3 surfaces: the deprecated Vercel exporter in server instrumentation and browser-side answer feedback. For JS/TS SDK v5.4+ the migration is:

• Replace langfuse-vercel with @langfuse/otel and register LangfuseSpanProcessor in packages/web/src/instrumentation.ts.
• Keep the current AI SDK telemetry and verify its trace ID still reaches the answer UI.
• Replace browser-side LangfuseWeb with LangfuseBrowserClient from @langfuse/browser, using its ingestion-backed .score(...) method for public-key feedback.
• Preserve boolean score data and a deterministic score ID so repeated feedback updates rather than duplicates.
• Run the flow against a self-hosted Langfuse URL as well as Cloud; keep browser feedback off management API methods that require newer self-hosted API support.

Guides: JS SDK v3→v4 and v4→v5.

If you need support with the migration, we're happy to jump on a call or help review a PR.