Restructure the agent_sdks folder

The code is reorganized with the following structure
```
agent_sdks/python
- src/a2ui
  - core
    - schema
      - manager.py
      - validation.py
      - payload_fixer.py
      - ...
    - template
      - ...
    - inference_stategy.py
  - adk
    - a2a_extension
      - a2ui_extension.py
      - send_a2ui_to_client_toolset.py
```

Tested:
- [x] All individual sample ADKs are working with connected client.
- [x] The orchestrator sample is also working with all sub-agents.

Author: nan-yu

a2a_agents/java/.gitignore agent_sdks/java/.gitignorea2a_agents/java/.gitignore renamed to agent_sdks/java/.gitignore

@@ -1,6 +1,13 @@
 # A2UI Agent implementation
 
-The `a2a_agents/python/a2ui_agent/` is the Python implementation of the a2ui agent library.
+The `agent_sdks/python/src/a2ui` is the Python implementation of the A2UI agent SDK library.
+
+## Core components (`src/a2ui/core`)
+
+The `src/a2ui/core` directory contains the core logic for the A2UI agent:
+
+*   **`a2ui_agent.py`**: The core A2UI agent class.
+*   **`a2ui_schema_utils.py`**: Schema manipulation helpers.
 
 ### Extension components (`src/a2ui/extension`)
 
@@ -12,10 +19,10 @@ The `src/a2ui/extension` directory contains the core logic for the A2UI agent ex
 
 ## Running tests
 
-1. Navigate to the a2ui_agent dir:
+1. Navigate to the directory:
 
    ```bash
-   cd a2a_agents/python/a2ui_agent
+   cd agent_sdks/python
    ```
 
 2. Run the tests
@@ -26,12 +33,20 @@ The `src/a2ui/extension` directory contains the core logic for the A2UI agent ex
 
 ## Building the SDK
 
-To build the SDK, run the following command from the `a2a_agents/python/a2ui_agent` directory:
+To build the SDK, run the following command from the `agent_sdks/python` directory:
 
 ```bash
 uv build .
 ```
 
+## Formatting code
+
+To format the code, run the following command from the `agent_sdks/python` directory:
+
+```bash
+uv run pyink .
+```
+
 ## Disclaimer
 
 Important: The sample code provided is for demonstration purposes and illustrates the mechanics of A2UI and the Agent-to-Agent (A2A) protocol. When building production applications, it is critical to treat any agent operating outside of your direct control as a potentially untrusted entity.

a2a_agents/java/pom.xml agent_sdks/java/pom.xmla2a_agents/java/pom.xml renamed to agent_sdks/java/pom.xml

@@ -21,7 +21,7 @@
 def load_constants(project_root):
   """Loads the shared constants module directly from its path in src/."""
   constants_path = os.path.join(
-      project_root, "src", "a2ui", "inference", "schema", "constants.py"
+      project_root, "src", "a2ui", "core", "schema", "constants.py"
   )
   if not os.path.exists(constants_path):
     raise RuntimeError(f"Could not find shared constants at {constants_path}")
@@ -39,14 +39,14 @@ class PackSpecsBuildHook(BuildHookInterface):
   def initialize(self, version, build_data):
     project_root = self.root
 
-    # Load constants dynamically from src/a2ui/inference/schema/constants.py
+    # Load constants dynamically from src/a2ui/core/schema/constants.py
     a2ui_constants = load_constants(project_root)
 
     spec_version_map = a2ui_constants.SPEC_VERSION_MAP
     a2ui_asset_package = a2ui_constants.A2UI_ASSET_PACKAGE
     specification_dir = a2ui_constants.SPECIFICATION_DIR
 
-    # project root is in a2a_agents/python/a2ui_agent
+    # project root is in agent_sdks/python
     # Dynamically find repo root by looking for specification_dir
     repo_root = a2ui_constants.find_repo_root(project_root)
     if not repo_root: