feat(settings): réglages Claude CLI (binaire + ~/.claude) & notif « disponible »

- Réglages → Claude CLI : override du chemin du binaire `claude` (effet à la
  prochaine session, fallback `which claude`), diagnostic de détection, et
  override de la racine ~/.claude (effet au redémarrage). Validateurs stricts.
- Push : notifie aussi sur le front busy→idle (session redevenue disponible).
- Renomme l'état affiché idle → « disponible » / « available » (web EN/FR + VS Code) ;
  l'enum SessionActivity du protocole reste inchangé.

packages/web/src/i18n/en.ts

@@ -56,7 +56,7 @@ export default {
     },
     registryStatus: {
       busy: 'busy',
-      idle: 'idle',
+      idle: 'available',
       waiting: 'waiting',
     },
     dialog: {
@@ -283,7 +283,7 @@ export default {
       live: 'Live',
       waiting: 'Waiting',
       busy: 'Busy',
-      idle: 'Idle',
+      idle: 'Available',
       exited: 'Exited',
       resumable: 'Resumable',
     },
@@ -413,6 +413,20 @@ export default {
     removeRoot: 'Remove',
     scanInterval: 'Re-scan interval (minutes)',
     scanIntervalHint: '0 disables periodic scanning. Changes apply on the next daemon restart.',
+    // Claude CLI
+    claudeCli: 'Claude CLI',
+    claudeCliHint: 'Where Arboretum finds the `claude` binary and its data. Handy when the daemon runs as a service with a minimal PATH that does not include ~/.local/bin.',
+    claudeBinStatusOk: 'Detected',
+    claudeBinStatusNotFound: 'Not found — sessions cannot start until this is resolved.',
+    claudeBinStatusBadPath: 'The configured path is not an executable file.',
+    claudeBinSourceConfigured: 'configured',
+    claudeBinSourcePath: 'PATH',
+    claudeBinPathLabel: 'Binary path override',
+    claudeBinPathHint: 'Absolute path to the `claude` executable. Leave empty to auto-detect via PATH. Takes effect on the next session.',
+    claudeBinPathPlaceholder: 'e.g. /home/you/.local/bin/claude',
+    claudeHomeLabel: 'Claude home directory',
+    claudeHomeHint: 'Override the ~/.claude location (transcripts & session registry). Applies on the next daemon restart.',
+    claudeHomePlaceholder: 'e.g. /home/you/.claude',
     // Serveur (lecture seule)
     server: 'Server',
     serverHint: 'Set at startup via CLI flags — changing them requires restarting the daemon.',