Add Auto permission mode (#63)

Adds Claude Code's auto permission mode as a fifth option between Accept Edits and Bypass, across terminals, resumed sessions, the tab badge, the scheduler task runner and docs. Warns that Auto falls back to prompting when unavailable for the model/backend.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

app/src/components/projects/home/TaskEditorModal.tsx

@@ -301,11 +301,18 @@ export default function TaskEditorModal({ project, task, onClose, onSaved }: Pro
             terminal attached, using this project’s permission mode (
             <strong className="text-[var(--text-primary)]">{modeLabel}</strong>).
           </p>
-          {mode !== "bypass" && (
+          {mode === "auto" && (
+            <p className="text-xs text-[var(--warning)]">
+              In Auto mode, actions the safety classifier blocks are denied and the run carries on
+              without them. If Auto isn&rsquo;t available for this project&rsquo;s model or backend,
+              Claude Code falls back to prompting and the task may stall.
+            </p>
+          )}
+          {mode !== "bypass" && mode !== "auto" && (
             <p className="text-xs text-[var(--warning)]">
               A headless run cannot answer a permission prompt. In {modeLabel} mode the task may
-              stall and produce an empty log; set the mode to Bypass in the Config tab for
-              unattended runs.
+              stall and produce an empty log; set the mode to Auto or Bypass in the Config tab
+              for unattended runs.
             </p>
           )}
         </div>