Handle additional error types in client initialization handling

[devcrocod]

May throw the following exceptions: CancellationException, McpException, StreamableHttpError, and SerializationException

Motivation and Context

This makes it possible to handle errors directly without needing to inspect the cause. For example:

try {
    client.connect(transport)
} catch (e: StreamableHttpError) {
    // ...
}

How Has This Been Tested?

locally

Breaking Changes

None

Types of changes

• Bug fix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to change)
• Documentation update

Checklist

• I have read the MCP Documentation
• My code follows the repository's style guidelines
• New and existing tests pass locally
• I have added appropriate error handling
• I have added or updated documentation as needed

[Copilot]

Pull Request Overview

This PR improves error handling in the MCP client initialization by allowing specific exception types to be thrown directly instead of being wrapped in IllegalStateException. This makes it easier for users to catch and handle specific error scenarios during client connection.

Key Changes:

• Modified the connect method's error handling to re-throw CancellationException, McpException, StreamableHttpError, and SerializationException directly
• Added imports for McpException and SerializationException
• Replaced if/else logic with a when expression for cleaner exception type checking

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[kpavlov]

Let's add a test

[kpavlov]

Cool, thank you!