(CODUX-142) Add weighted task progress calculator

[numnx]

🧩 Task: Add weighted task progress calculator

Automated task PR opened by Code UX for T01.

📋 Summary

Sprint: Sprint 204 · Sprint Progress · Task: T01

Expose live weighted sprint completion using task lifecycle stages and coding tool-call telemetry, preserve raw completed-task counts, and refresh/render fractional progress accurately across the dashboard and documentation.

🤖 Model & Provider

Provider	Codex CLI
Model	gpt-5.6-sol

⏱️ Timing

Started	2026-07-11 02:13:23 UTC
Finished	2026-07-11 02:20:26 UTC
Duration	7m 3s

📊 Token Usage

Metric	Value
Input tokens	78,109
Cached input tokens	1,371,136
Output tokens	9,794
Total tokens	1,459,039
Invocations	2
Tool calls	23
Active time	6m 7s

Included usage estimate (subscription/local login): $1.37

✅ QA Review

⏳ QA review runs after this PR is opened. Check the task card in the dashboard for the outcome once it lands.

📝 Full Task Prompt

## Objective
Add a side-effect-free task progress calculator for the sprint weighting rules in CODUXCODUX-142.

## Scope
- `src/domain/sprint/sprint-progress.ts`
- `tests/backend/domain/sprint/sprint-progress.test.ts`
- Task status and merge-indicator values from `src/contracts/project-management-types.ts` and `src/contracts/app-types.ts`

## Implementation Requirements
1. Define the task weights: pending contributes `0`, coding contributes up to `0.5`, CI/post-coding gate progress contributes `0.75`, and settled completion contributes `1.0`.
2. For tasks still coding, add `0.005` per coding provider tool call, clamp the count at 100, and ignore negative or invalid counts.
3. Treat `completed`, merged states, and canonical settled merge indicators as full completion; treat `CI`, `QA_PENDING`, `MERGE_BLOCKED`, and `MERGE_CONFLICT` as post-coding progress; keep `coding_completed` at `0.5` and preserve partial tool-call progress for unfinished coding states.
4. Add focused tests for empty tasks, 100-call capping, coding completion, CI progress, no-CI completion jumps, settled merge states, and mixed task totals rounded to one decimal percentage point.

## Constraints
- Keep the helper pure and reusable from repository read models.
- Align state interpretation with `src/domain/sprint/task-pipeline-stage.ts`; do not change task lifecycle transitions.
- Do not add a database column or migration for derived sprint progress.

## Verification
- Run `pnpm run test:backend -- tests/backend/domain/sprint/sprint-progress.test.ts`.
- Run `pnpm run typecheck` and confirm the helper and tests compile without new errors.

🌿 Branch Info

Base: feature/CODUX-204-sprint-progress
Head: task/feature-codux-20-t01-codex-7bfb17f7-mrfqd1rq

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🤖 Generated by Code UX