docs(web-client): Add Private Note Transfer tutorial with Note Transport Service and fetchPrivate()

[mehmetkr-31]

Problem / Context

Under docs/src/web-client/, there are runnable web tutorials for public note operations (mint_consume_create_tutorial.md), counter contracts, and foreign procedure invocations, but no tutorial for Private Note transfers.

In addition, existing notes in mint_consume_create_tutorial.md state that private notes must be exchanged manually out-of-band. Now that @miden-sdk/miden-sdk natively supports client.notes.sendPrivateNote() and client.notes.fetchPrivate() via the Note Transport Service, web dApp developers need a dedicated, end-to-end tutorial.

Proposed Solution

Add a new step-by-step tutorial at docs/src/web-client/private_notes_tutorial.md demonstrating:

1. Initializing MidenClient from @miden-sdk/miden-sdk in a Vite/React web app.
2. Creating and sending a private P2ID note using client.notes.sendPrivateNote().
3. Transporting note metadata and fetching recipient private notes via client.notes.fetchPrivate().
4. Consuming the private note on the recipient web client and asserting updated account vault balances.
5. Updating outdated private note disclaimers in mint_consume_create_tutorial.md to link to this new tutorial.

Expected Impact

Fills the missing web tutorial gap and provides frontend developers with a runnable TypeScript reference for Miden's flagship privacy feature.

I would like to write and submit this tutorial. Could a maintainer please assign this issue to me?