feat: add Claude Code detected/missing badge to status bar

Uses the existing check_claude_cli Tauri command to detect the claude
binary at app startup and shows a status badge — green/neutral when
found, orange warning when missing with a click-to-install link.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

src/hooks/useClaudeCodeStatus.ts

@@ -0,0 +1,41 @@
+import { useEffect, useState } from 'react'
+import { invoke } from '@tauri-apps/api/core'
+import { isTauri, mockInvoke } from '../mock-tauri'
+
+export type ClaudeCodeStatus = 'checking' | 'installed' | 'missing'
+
+interface ClaudeCliResult {
+  installed: boolean
+  version: string | null
+}
+
+function tauriCall<T>(command: string): Promise<T> {
+  return isTauri() ? invoke<T>(command) : mockInvoke<T>(command)
+}
+
+/**
+ * Checks once on mount whether the `claude` CLI binary is available.
+ * Returns a status suitable for the status bar badge.
+ */
+export function useClaudeCodeStatus(): { status: ClaudeCodeStatus; version: string | null } {
+  const [status, setStatus] = useState<ClaudeCodeStatus>('checking')
+  const [version, setVersion] = useState<string | null>(null)
+
+  useEffect(() => {
+    let cancelled = false
+
+    tauriCall<ClaudeCliResult>('check_claude_cli')
+      .then((result) => {
+        if (cancelled) return
+        setStatus(result.installed ? 'installed' : 'missing')
+        setVersion(result.version ?? null)
+      })
+      .catch(() => {
+        if (!cancelled) setStatus('missing')
+      })
+
+    return () => { cancelled = true }
+  }, [])
+
+  return { status, version }
+}