feat: replace custom duration utils with qte library

[adelrodriguez]

Greptile Summary

This PR replaces custom duration utilities with the qte library, a specialized TypeScript package for time expressions. The custom implementation in packages/utils/src/duration.ts (251 lines) has been removed along with its comprehensive test suite and session constants.

Key Changes:

• Removed milliseconds() and seconds() functions from @init/utils/duration in favor of ms() and seconds() from qte
• Changed type from DurationInput to TimeExpression across the codebase
• Replaced hardcoded session constants (SESSION_EXPIRES_IN, SESSION_UPDATE_AGE) with inline duration strings (seconds("30d"), seconds("15d"))
• Added qte@0.1.0 as a dependency to 4 packages (api, backend, email, kv)
• Removed @init/error dependency from @init/kv package (no longer needed without custom duration utilities)

Confidence Score: 5/5

• This PR is safe to merge with minimal risk
• The refactoring is comprehensive and consistent across all usages. The migration from custom duration utilities to the qte library is straightforward with equivalent API surface. All imports have been updated correctly, and there are no remaining references to the old implementation.
• No files require special attention

Important Files Changed

Filename	Overview
packages/utils/src/duration.ts	Removed custom duration utilities in favor of qte library
apps/api/src/shared/auth.ts	Migrated from constants to inline seconds("30d") and seconds("15d") calls using qte
apps/api/src/shared/middleware.ts	Changed type from DurationInput to TimeExpression and function from milliseconds() to ms()
packages/backend/src/functions/shared/auth/options.ts	Migrated session config to use qte seconds() function with inline duration strings
packages/email/src/client.ts	Updated type from DurationInput to TimeExpression and function from milliseconds() to ms()
packages/kv/src/client.ts	Migrated to qte library, changed type to TimeExpression and uses seconds() function

Flowchart

%%{init: {'theme': 'neutral'}}%%
flowchart TD
    A[Custom Duration Utils] -->|Removed| B[qte Library v0.1.0]
    B --> C[Auth Session Config]
    B --> D[Rate Limiting]
    B --> E[KV Client TTL]
    B --> F[Email Scheduling]
    
    C -->|seconds 30d| C1[apps/api auth.ts]
    C -->|seconds 15d| C2[packages/backend auth options]
    
    D -->|ms interval| D1[apps/api middleware.ts]
    
    E -->|seconds ttl| E1[packages/kv client.ts]
    
    F -->|ms sendAt| F1[packages/email client.ts]
    
    style A fill:#ff6b6b
    style B fill:#51cf66

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[adelrodriguez]

• refactor: replace better-result with faultier for error handling #94 : 2 dependent PRs (#95 , #98 )
• refactor: move MOBILE_BREAKPOINT from utils to ui package #93
• refactor: move THEMES constant from utils to ui package #92
• refactor: move environment prefix constants from utils to env package #91
• feat: replace custom duration utils with qte library #90 👈 (View in Graphite)
• main

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