Revise DirectConnector branding and README to reflect current SDK architecture

The `DirectConnector` name is inherited from the early prototype that directly accessed API Hub before the Connectors SDK or AI Gateway existed. This branding is likely to cause confusion now.

Tasks:
- Rename the project folder and namespace from `DirectConnector` to something more descriptive (e.g., `ConnectorsSample`, `FunctionsConnectorSample`)
- Update the README content to better reflect the current SDK-based architecture
- Remove historical artifacts and terminology that reference the old direct-access approach
- Update the solution file project reference

Start by locating the DirectConnector project folder, its namespace declarations, the README, and the solution file project reference. Review the existing terminology and SDK architecture described in the repository before choosing a replacement name. Done means the folder, namespace, README, historical references, and solution reference consistently use the new branding.

Written by the indexing model from the issue text.