fix(api): weight self-hosted analytics avg response time by request count

[shuvamk]

Problem

server_analytics.response_time is documented in the schema as a per-minute average response time (seconds). The self-hosted analytics reducers average those per-minute averages unweighted — dividing by the number of minute-buckets rather than by total requests. So a period's avgResponseTimeMs is wrong whenever minutes carry unequal traffic.

The OpenShip Cloud path already does this correctly: summariseCloudBuckets / buildCloudHourlyPeriods compute response_time_sum / requests (request-weighted). Only the self-hosted path (summariseBuckets / buildHourlyPeriods) was unweighted — so self-hosters see a distorted number that the cloud dashboard does not.

Concrete failing input

Two minutes inside one period:

minute	requests	per-minute avg
0	1	1000 ms
1	99	100 ms

	avgResponseTimeMs
Correct (request-weighted: (1·1000 + 99·100)/100)	109 ms
Reported before this fix ((1000 + 100)/2)	550 ms

A single slow request in an otherwise-quiet minute drags the whole period's reported latency up ~5×.

Fix

summariseBuckets and buildHourlyPeriods now weight each minute by its request count and divide by total requests — the same computation the cloud path already uses. Both guard a zero-request period so it returns 0 instead of NaN (again matching summariseCloudBuckets). No wire/DB shape changes; the two pure functions are exported so they can be unit-tested (existing precedent in this repo).

Tests

Added apps/api/test/modules/analytics/response-time-weighting.test.ts:

• summariseBuckets and buildHourlyPeriods report the request-weighted 109 ms for the table above.
• A no-traffic period reports 0, not NaN.

Verified the test fails against unpatched source (reports 550 ms) and passes with the fix.

Verification

• bun run test → all 6 turbo tasks successful (748 passed in @repo/api, incl. the 3 new tests).
• bun run --cwd apps/api lint → clean.
• Touched files pass npx prettier --check; the file has two pre-existing unrelated drifts on main (an import block and a queryBuckets call) that I deliberately left untouched to keep the diff surgical.