feat(analytics): add latency histogram buckets to analytics summary

[brodapeethar]

Summary

Adds latency bucket counts to the analytics API to provide investor-grade performance visibility for paid query execution. Analytics now returns execution time distribution across five latency bands without changing provider execution or payment behavior.

Changes

• packages/shared/src/types.ts — Added LatencyBucket type ("<1s" | "1-3s" | "3-10s" | ">10s" | "unknown") and latencyBuckets: Record<LatencyBucket, number> to AnalyticsSummary
• apps/api/src/lib/storage/serialization.ts — Implemented classifyLatency() and bucket computation in buildAnalyticsSummary(); zeroed buckets on empty storage; unknown/missing latency counted separately
• apps/web/src/types.ts — Added latencyBuckets to AnalyticsResponse using the shared LatencyBucket type
• apps/api/src/routes/public.test.ts — Updated empty-storage test to assert zeroed buckets; added dedicated test covering fast (500ms), medium (2s), slow (5s), very-slow (15s), and unknown (0ms) records

Closes

Closes #89

[vercel]

@brodapeethar is attempting to deploy a commit to the emrekayat's projects Team on Vercel.

A member of the Team first needs to authorize it.

[emrekayat]

Thanks for the PR. I checked this from the emrekayat account.

I cannot run a proper merge-ref review or merge it yet because GitHub reports the branch as CONFLICTING / DIRTY, and refs/pull/96/merge is not available. Please rebase or merge the latest main and resolve the conflicts first.

Once it is mergeable, I will recheck the analytics latency bucket logic, shared/web types, and the API tests.

[drips-wave]

@brodapeethar Great news! 🎉 Based on an automated assessment of this PR, the linked Wave issue(s) no longer count against your application limits.

You can now already apply to more issues while waiting for a review of this PR. Keep up the great work! 🚀

Learn more about application limits

[brodapeethar]

@emrekayat please review and merge

[emrekayat]

Thanks for the update. I rechecked the latest merge ref from the maintainer account after #112 landed, but this still is not merge-ready.

Commands run:

git diff --check main...pr-96-merge
npm run test --workspace @query402/shared
npm run test --workspace @query402/api -- src/routes/public.test.ts

Shared tests pass, but the API public route test fails:

public routes > returns latency bucket counts that classify queries by execution time
AssertionError: expected undefined to deeply equal { "<1s": 1, "1-3s": 1, "3-10s": 1, ">10s": 1, "unknown": 1 }

The new latencyBuckets data is not present in the /api/analytics response shape on the current merge ref. Please wire the computed buckets into the public analytics response and make sure it remains compatible with the newly merged price-outlier analytics fields.