docs: simplify examples by using default import replicate pattern

- Remove explicit `replicate = Replicate()` from most examples
- Use `import replicate` pattern which automatically uses REPLICATE_API_TOKEN
- Keep one comprehensive example showing custom client configuration with environment variables
- Maintain explicit client instantiation only where showing advanced configuration
- Update Quick Start, Type Hints, and Migration Guide sections accordingly

This makes the examples cleaner and follows the most common usage pattern
where users rely on the default environment variable configuration.

Author: zeke

api.md

@@ -9,10 +9,7 @@ pip install replicate
 ## Quick Start
 
 ```python
-from replicate import Replicate
-
-# Initialize with REPLICATE_API_TOKEN env var by default
-replicate = Replicate()
+import replicate
 
 # Create a model function
 banana = replicate.use("google/nano-banana")
@@ -30,37 +27,45 @@ output = replicate.run(
 
 ## Client Initialization
 
-### Synchronous Client
+By default, the SDK uses the `REPLICATE_API_TOKEN` environment variable:
 
 ```python
-from replicate import Replicate
+import replicate
 
-# Using environment variable (REPLICATE_API_TOKEN)
-replicate = Replicate()
+# Uses REPLICATE_API_TOKEN from environment
+output = replicate.run("google/nano-banana", input={"prompt": "hello"})
+```
+
+### Custom Client Configuration
 
-# With explicit token
-replicate = Replicate(bearer_token="your_api_token")
+For advanced use cases, you can create an explicit client instance:
 
-# Legacy token parameter (for compatibility)
-replicate = Replicate(api_token="your_api_token")
+```python
+from replicate import Replicate
+import os
 
-# With custom configuration
+# Explicitly specify which environment variable to use
 replicate = Replicate(
-    bearer_token="your_api_token",
+    bearer_token=os.environ.get("MY_REPLICATE_TOKEN"),
     base_url="https://api.replicate.com/v1",  # Optional custom base URL
     timeout=120.0,  # Request timeout in seconds
     max_retries=5  # Maximum number of retries
 )
+
+# Now use this configured client
+output = replicate.run("google/nano-banana", input={"prompt": "hello"})
 ```
 
 ### Asynchronous Client
 
 ```python
 from replicate import AsyncReplicate
 import asyncio
+import os
 
 async def main():
-    replicate = AsyncReplicate(bearer_token="your_api_token")
+    # Can specify token explicitly if needed
+    replicate = AsyncReplicate(bearer_token=os.environ.get("MY_REPLICATE_TOKEN"))
     output = await replicate.run(
         "google/nano-banana",
         input={"prompt": "a watercolor painting"}
@@ -664,12 +669,10 @@ The SDK respects these environment variables:
 The SDK is fully typed with comprehensive type hints:
 
 ```python
-from replicate import Replicate
+import replicate
 from replicate.types import Prediction, PredictionStatus
 from replicate.pagination import SyncCursorURLPage
 
-replicate: Replicate = Replicate()
-
 # Type hints for responses
 prediction: Prediction = replicate.predictions.get(prediction_id="abc123")
 status: PredictionStatus = prediction.status
@@ -708,6 +711,7 @@ from replicate import AsyncReplicate
 
 async def batch_process(prompts):
     """Process multiple prompts in parallel."""
+    from replicate import AsyncReplicate
     replicate = AsyncReplicate()
     tasks = [
         replicate.run("model:version", input={"prompt": prompt})
@@ -780,9 +784,7 @@ model = replicate.models.get("google/nano-banana")
 
 **New (v1.0+):**
 ```python
-from replicate import Replicate
-
-replicate = Replicate()
+import replicate
 
 # Run a model
 output = replicate.run(
@@ -802,6 +804,8 @@ model = replicate.models.get(
 For compatibility with older code:
 
 ```python
+from replicate import Replicate
+
 # Old style (still supported)
 replicate = Replicate(api_token="your_token")