Restructure client docs into Rust / Web / React three-tier hierarchy

Source: DevEx Sync (Notion).

Wiktor is splitting the client docs into three hierarchies — Rust client, Web client, React client — matching the Rust documentation approach (initialization, account APIs, transactions, notes per surface).

Currently:

- Rust client is ingested from `miden-client/` and follows the canonical hierarchy.
- Web client and React SDK pages are authored locally in this repo and have a less consistent shape.

Scope:

- Define and document the canonical three-tier IA (Rust / Web / React) with parallel sub-page structure.
- Reorganise existing Web client + React SDK pages into that structure.
- Ensure `deploy-docs.yml` ingestion paths still preserve the locally-authored Web/React siblings.

Upstream dependency: coordinated with Wiktor's `miden-client` repo split. Ship the docs IA in lockstep with the SDK split.