refactor(observability): unify timing instrumentation across runtimes

[limityan]

Summary

• Add shared timing helpers for Web UI and Rust core.
• Merge debugProbe back into the shared logger/timing path and normalize frontend diagnostic fields to durationMs.
• Replace representative ad-hoc timing code in frontend and backend modules with shared helpers.
• Add a few low-noise timing logs for slow filesystem operations, context compression, and snapshot completion.
• Update frontend and backend logging guidance for future instrumentation work.

Why

• Timing diagnostics had started to drift across multiple patterns, which made filtering, grep, and later cleanup harder.
• We wanted better visibility into a few important execution paths without adding high-frequency logging noise or changing protocol-level duration fields.

Scope

• Frontend:
  • add src/web-ui/src/shared/utils/timing.ts
  • converge debugProbe and representative startup/i18n/LSP/API/git/editor/terminal timing sites onto shared helpers
• Backend:
  • add src/crates/core/src/util/timing.rs
  • reuse shared elapsed helpers in representative desktop/core/ai-adapters call sites
  • enrich existing completion logs with duration metadata where it improves diagnosis without increasing log volume
• Documentation:
  • update src/web-ui/LOGGING.md
  • update src/crates/LOGGING.md

Non-Goals

• No protocol or persisted field renames such as duration_ms, execution_time_ms, or response_time_ms.
• No broad migration of animation, scroll, polling, or deadline control-flow timing.
• No attempt to add exhaustive timing logs everywhere.

Verification

• pnpm --dir src/web-ui exec eslint src/main.tsx src/infrastructure/i18n/core/I18nService.ts src/shared/utils/timing.ts src/shared/utils/debugProbe.ts src/shared/utils/index.ts src/tools/lsp/services/LspService.ts src/tools/lsp/services/LspExtensionRegistry.ts src/tools/lsp/services/LspDiagnostics.ts src/flow_chat/services/EventBatcher.ts src/app/hooks/useWindowControls.ts src/tools/terminal/components/Terminal.tsx src/tools/git/state/GitStateManager.ts src/tools/git/services/GitService.ts src/tools/editor/components/CodeEditor.tsx src/tools/editor/components/MarkdownEditor.tsx src/infrastructure/api/service-api/ApiClient.ts
• pnpm --dir src/web-ui exec tsc --noEmit
• cargo check -p bitfun-core -p bitfun-desktop -p bitfun-ai-adapters