fix(agent): raise tool rounds and ease calendar creates

Local models were burning the 8-round budget on simple event adds.
Raise the limit, resolve calendars by name/default, and inject the
household clock so relative dates work.

tests/unit/agent-chat.test.ts

@@ -83,6 +83,36 @@ describe("runAgentChat", () => {
     assert.equal(result.message.role, "assistant");
     assert.ok(result.message.content.length > 0);
   });
+
+  it("appends runtime clock context to the system prompt", async () => {
+    const original = process.env.HOUSEHOLD_TIMEZONE;
+    process.env.HOUSEHOLD_TIMEZONE = "America/Chicago";
+
+    let systemContent = "";
+    const result = await runAgentChat({
+      messages: [{ role: "user", content: "hello" }],
+      request: new Request("http://localhost:3000/api/agent/chat"),
+      systemPrompt: "You are a pirate.",
+      llm: {
+        async chatCompletion(request) {
+          const system = request.messages.find((message) => message.role === "system");
+          systemContent = typeof system?.content === "string" ? system.content : "";
+          return {
+            message: { role: "assistant", content: "Ahoy" },
+            finishReason: "stop",
+          };
+        },
+      },
+    });
+
+    assert.equal(result.message.content, "Ahoy");
+    assert.match(systemContent, /^You are a pirate\./);
+    assert.match(systemContent, /Current time:/);
+    assert.match(systemContent, /America\/Chicago/);
+
+    if (original === undefined) delete process.env.HOUSEHOLD_TIMEZONE;
+    else process.env.HOUSEHOLD_TIMEZONE = original;
+  });
 });
 
 it("passes a model override to the OpenAI-compatible client", async () => {