Fix agent lifecycle example output to reflect correct hook execution order (#1015)

**Problem:**
The expected output in the agent lifecycle example incorrectly shows
agent start hooks (`on_start`) running after tool execution and multiple
times for the same agent. This misleads developers about when these
lifecycle events actually occur.

**Solution:**
Updated the expected output to accurately reflect the OpenAI Agents
framework behavior:
- Agent start hooks run immediately when an agent begins execution
- Start hooks only run once per agent activation, controlled by the
`should_run_agent_start_hooks` flag
- After handoffs, the new agent's start hook runs as the first event

Author: DanielHashmi

examples/basic/agent_lifecycle_example.py

@@ -101,12 +101,10 @@ async def main() -> None:
 ### (Start Agent) 1: Agent Start Agent started
 ### (Start Agent) 2: Agent Start Agent started tool random_number
 ### (Start Agent) 3: Agent Start Agent ended tool random_number with result 37
-### (Start Agent) 4: Agent Start Agent started
-### (Start Agent) 5: Agent Start Agent handed off to Multiply Agent
+### (Start Agent) 4: Agent Start Agent handed off to Multiply Agent
 ### (Multiply Agent) 1: Agent Multiply Agent started
 ### (Multiply Agent) 2: Agent Multiply Agent started tool multiply_by_two
 ### (Multiply Agent) 3: Agent Multiply Agent ended tool multiply_by_two with result 74
-### (Multiply Agent) 4: Agent Multiply Agent started
-### (Multiply Agent) 5: Agent Multiply Agent ended with output number=74
+### (Multiply Agent) 4: Agent Multiply Agent ended with output number=74
 Done!
 """

examples/basic/lifecycle_example.py

@@ -105,14 +105,12 @@ async def main() -> None:
 Enter a max number: 250
 ### 1: Agent Start Agent started. Usage: 0 requests, 0 input tokens, 0 output tokens, 0 total tokens
 ### 2: Tool random_number started. Usage: 1 requests, 148 input tokens, 15 output tokens, 163 total tokens
-### 3: Tool random_number ended with result 101. Usage: 1 requests, 148 input tokens, 15 output tokens, 163 total tokens
-### 4: Agent Start Agent started. Usage: 1 requests, 148 input tokens, 15 output tokens, 163 total tokens
-### 5: Handoff from Start Agent to Multiply Agent. Usage: 2 requests, 323 input tokens, 30 output tokens, 353 total tokens
-### 6: Agent Multiply Agent started. Usage: 2 requests, 323 input tokens, 30 output tokens, 353 total tokens
-### 7: Tool multiply_by_two started. Usage: 3 requests, 504 input tokens, 46 output tokens, 550 total tokens
-### 8: Tool multiply_by_two ended with result 202. Usage: 3 requests, 504 input tokens, 46 output tokens, 550 total tokens
-### 9: Agent Multiply Agent started. Usage: 3 requests, 504 input tokens, 46 output tokens, 550 total tokens
-### 10: Agent Multiply Agent ended with output number=202. Usage: 4 requests, 714 input tokens, 63 output tokens, 777 total tokens
+### 3: Tool random_number ended with result 101. Usage: 1 requests, 148 input tokens, 15 output tokens, 163 total token
+### 4: Handoff from Start Agent to Multiply Agent. Usage: 2 requests, 323 input tokens, 30 output tokens, 353 total tokens
+### 5: Agent Multiply Agent started. Usage: 2 requests, 323 input tokens, 30 output tokens, 353 total tokens
+### 6: Tool multiply_by_two started. Usage: 3 requests, 504 input tokens, 46 output tokens, 550 total tokens
+### 7: Tool multiply_by_two ended with result 202. Usage: 3 requests, 504 input tokens, 46 output tokens, 550 total tokens
+### 8: Agent Multiply Agent ended with output number=202. Usage: 4 requests, 714 input tokens, 63 output tokens, 777 total tokens
 Done!
 
 """