Add Auto permission mode

Claude Code now ships `--permission-mode auto`, where a safety classifier
approves routine actions and blocks risky ones without prompting. Expose it
as a fifth mode between Accept Edits and Bypass: terminals, resumed sessions,
the tab badge, and the scheduler's task runner all map it to the flag.

Headless scheduled runs don't stall in Auto (blocked actions are denied, not
prompted), so the task editor shows a softer note instead of the stall warning.

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

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

@@ -159,12 +159,18 @@ describe("TaskEditorModal", () => {
   });
 
   it("warns that a headless run cannot answer a permission prompt", async () => {
-    // Bypass is the only mode where an unattended run is safe from stalling.
+    // Bypass (and Auto, below) are the modes where an unattended run cannot stall.
     await renderEditor(null, { ...baseProject, permission_mode: "bypass" });
     expect(screen.getByText(/headless/i)).toBeInTheDocument();
     expect(screen.queryByText(/cannot answer a permission prompt/i)).toBeNull();
   });
 
+  it("tells Auto mode that blocked actions are denied, not prompted", async () => {
+    await renderEditor(null, { ...baseProject, permission_mode: "auto" });
+    expect(screen.queryByText(/cannot answer a permission prompt/i)).toBeNull();
+    expect(screen.getByText(/blocks are denied/i)).toBeInTheDocument();
+  });
+
   it("spells out the stall risk in any non-Bypass mode", async () => {
     await renderEditor(null, { ...baseProject, permission_mode: "default" });
     expect(screen.getByText(/cannot answer a permission prompt/i)).toBeInTheDocument();