docs: update README with lifespan examples and usage

Add comprehensive documentation for lifespan support:
- Add usage examples for both Server and FastMPC classes
- Document startup/shutdown patterns
- Show context access in tools and handlers
- Clean up spacing in test files

tests/server/fastmcp/test_func_metadata.py

@@ -236,7 +236,7 @@ async def test_lambda_function():
 
 def test_complex_function_json_schema():
     """Test JSON schema generation for complex function arguments.
-    
+
     Note: Different versions of pydantic output slightly different
     JSON Schema formats for model fields with defaults. The format changed in 2.9.0:
 
@@ -245,16 +245,16 @@ def test_complex_function_json_schema():
          "allOf": [{"$ref": "#/$defs/Model"}],
          "default": {}
        }
-       
+
     2. Since 2.9.0:
        {
          "$ref": "#/$defs/Model",
          "default": {}
        }
-       
+
     Both formats are valid and functionally equivalent. This test accepts either format
     to ensure compatibility across our supported pydantic versions.
-    
+
     This change in format does not affect runtime behavior since:
     1. Both schemas validate the same way
     2. The actual model classes and validation logic are unchanged
@@ -262,17 +262,17 @@ def test_complex_function_json_schema():
     """
     meta = func_metadata(complex_arguments_fn)
     actual_schema = meta.arg_model.model_json_schema()
-    
+
     # Create a copy of the actual schema to normalize
     normalized_schema = actual_schema.copy()
-    
+
     # Normalize the my_model_a_with_default field to handle both pydantic formats
-    if 'allOf' in actual_schema['properties']['my_model_a_with_default']:
-        normalized_schema['properties']['my_model_a_with_default'] = {
-            '$ref': '#/$defs/SomeInputModelA',
-            'default': {}
+    if "allOf" in actual_schema["properties"]["my_model_a_with_default"]:
+        normalized_schema["properties"]["my_model_a_with_default"] = {
+            "$ref": "#/$defs/SomeInputModelA",
+            "default": {},
         }
-    
+
     assert normalized_schema == {
         "$defs": {
             "InnerModel": {