Add React SDK TypeScript Client tutorial for account state and balances

## Problem

Pioneer feedback called out that there is no obvious, working React SDK example for common app flows such as fetching the connected wallet account and rendering balances.

These examples should be runnable from this repository and then surfaced in the docs site through the tutorial ingestion flow.

## Decision

Use `0xMiden/tutorials` as the source of truth for runnable React SDK / TypeScript Client tutorials. The docs repo should link to or ingest these pages, while keeping API/reference material in the docs repo.

Also prefer the user-facing label "TypeScript Client" over "Web Client" for the tutorial/recipe section, while keeping browser/WASM-specific caveats in the content.

## Proposed scope

- Add a runnable React SDK tutorial for account state and balances.
- Cover provider setup, client readiness, connected/active account selection, sync before reads, balance rendering, loading/error/empty states, and refresh after transactions.
- Include a minimal working UI in `web-client/` that can be exercised locally.
- Update the source tutorial docs under `docs/src/web-client` or perform a careful rename to `docs/src/typescript-client` if the docs ingestion path is updated at the same time.
- Link back to the React SDK reference docs in `0xMiden/docs`.
- Include `useExecuteProgram()` only if it is available in the current shipped React SDK and can be validated.

## Acceptance criteria

- A developer can run the tutorial from a clean checkout and see the account/balance flow working.
- The tutorial includes copy-pasteable React SDK code using the current `@miden-sdk/react` package API.
- The docs source clearly distinguishes React hooks from lower-level TypeScript/WebClient APIs.
- The example is validated in a clean Docker environment; use Playwright for the browser flow where practical.
- The tutorial is ready to be ingested into the main docs site.

## Related

- 0xMiden/docs#275