Rename task update tool to patch_tasks

tests/prompt.test.ts

@@ -100,7 +100,7 @@ test("keeps task guidance short with planning after exploration", () => {
   assert.match(prompt, /then call set_tasks before implementation/);
   assert.match(prompt, /otherwise skip tracking/);
   assert.match(prompt, /Start one task in-progress/);
-  assert.match(prompt, /update_task when tasks start, block, or finish/);
+  assert.match(prompt, /patch_tasks when tasks start, block, or finish/);
   assert.match(prompt, /keep statuses accurate before the final response/);
   assert.ok(prompt.split(/\s+/).length < 40);
 });
@@ -179,8 +179,8 @@ test("session_compact sends one hidden reminder only for unfinished tasks", asyn
     },
   ]);
 
-  await tools.get("update_task").execute(
-    "update",
+  await tools.get("patch_tasks").execute(
+    "patch",
     { tasks: [{ id: 1, status: "done" }] },
     undefined,
     undefined,