Fix desktop workspace chat root mismatches

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Summary

• Fixes a critical desktop workspace data split where agent-rpc wrote chat data under <workspace>/chat, while Tauri host helpers reloaded transcripts, sessions, memory/logs, and prompt artifacts from the process-global chat root.
• Fixes Life Pulse rhythm execution so due scheduled jobs are executed with schedule tick --workspace <workspace> from the resolved project root, matching the due-check workspace.
• The approach keeps old omitted-workspace calls compatible by centralizing an optional workspace chat-root helper: supplied workspace => <project>/chat, omitted workspace => legacy process-global chat root.

Task Linkage

• Task ID: TASK-2026-070
• Task folder: tasks/TASK-2026-070-desktop-workspace-root-fixes/

Injected Specs

• spec/architecture-boundaries.md (desktop command/bridge routing reviewed; no dependency direction changes)
• spec/security-nonnegotiables.md (not a sandbox/security policy change)
• spec/testing-policy.md (required for Rust/frontend code change)
• spec/docs-sync.md (reviewed; no docs needed because this restores intended behavior without new commands/flags/env vars)
• Additional injected specs followed: spec/verification-integrity.md, spec/task-artifact-language.md, spec/structured-signal-first.md, spec/capability-gap-evolution.md.

Validation Evidence

• Commands executed:
  • rustup update stable && rustup default stable
  • npm ci
  • cargo fmt --check
  • npm run build in crates/skilllite-assistant
  • cargo test --manifest-path crates/skilllite-assistant/src-tauri/Cargo.toml
  • cargo clippy --manifest-path crates/skilllite-assistant/src-tauri/Cargo.toml --all-targets -- -A dead_code -A unused_imports -D warnings
  • cargo test
  • cargo clippy --all-targets -- -D warnings
  • python3 scripts/validate_tasks.py
• Key results:
  • Frontend build: ✓ built in 1.99s.
  • Tauri tests: 58 passed; 0 failed (includes new workspace chat root, prompt diff, session, and rhythm arg tests).
  • Root cargo tests: completed successfully.
  • Root clippy: completed successfully with -D warnings.
  • Tauri clippy: passed after allowing existing dead_code / unused_imports categories that block this manifest independently of this PR.
  • Task validation: Task validation passed (70 task directories checked).

Regression Scope

• Areas likely affected:
  • Desktop transcript reload, sessions sidebar CRUD/listing, recent memory/log/prompt panels, evolution prompt diff/manual edit, Life Pulse schedule execution.
• Explicit non-goals:
  • CLI-only evolution maintenance commands (reset, disable, explain, repair-skills).
  • Sandbox policy, LLM routing, or non-desktop CLI data-root semantics.

Docs Sync (EN/ZH)

• Not needed
• Updated EN + ZH docs
• Files:
  • N/A

Review Checklist

• Acceptance criteria in tasks/TASK-2026-070-desktop-workspace-root-fixes/TASK.md satisfied
• tasks/TASK-2026-070-desktop-workspace-root-fixes/STATUS.md updated with latest progress
• tasks/TASK-2026-070-desktop-workspace-root-fixes/REVIEW.md includes merge readiness decision
• tasks/board.md status is up to date