Corrections needed for getting-started.mdx

[RomThpt]

Description:
The getting-started.mdx file in the cartridge-docs repository requires corrections. Please review and update the content as needed.

Issues Identified:

Basic Usage Section:

Change the example
Usage with Starknet React Section:

Check the integration code with starknet-react.
Ensure the ControllerConnector and StarknetConfig are used properly.

Examples Section:
Verify the links to the integration guides for React, Svelte, and Rust.
Ensure the examples are comprehensive and follow best practices.

Proposed Corrections:
Correct errors in the example code.
Ensure all descriptions and steps are clear and concise.

Additional Notes:
Please review the recent commits for additional context and changes made to this file.