client.ts: Document all public SplitClient methods with JSDoc

[Kingsman-99]

Description

src/client.ts is the primary entry point for SDK consumers, but the SplitClient class methods lack JSDoc. This forces new integrators to read the source to understand how to use the SDK, increasing time to integration.

Acceptance Criteria

• Every public method on SplitClient has a JSDoc block with @param, @returns, and @throws tags
• At least the three most commonly used methods include a @example block
• Private methods are left without JSDoc (or given minimal /** @internal */ tags)
• Unit tests pass

Context

• Target file: src/client.ts
• Documentation only; no method signatures or behaviors may change