Show loading state when saving private pass to wallet

When saving a private pass to the wallet, the operation involves an
asynchronous backend call.

This patch updates the Autofill AI add/edit dialog to handle the
asynchronous nature of saving to the wallet. Specifically, it:
* Updates `addOrUpdateEntityInstance` in the data manager proxy and private API definitions to return a `Promise<void>`.
* Adds a `saveInProgress_` property to track the operation status.
* Displays a spinner on the "Save" button and hides the button text while saving is active.
* Disables the "Cancel" button during the save operation to prevent inconsistent states.
* Exposes the `autofillAiWalletPrivatePasses` feature flag to the WebUI to control this behavior.

Screencast: https://screencast.googleplex.com/cast/NjU1NjkyNzYzMzkxNTkwNHw2OTUxYWJmZS0xNQ

Bug: 477845712
Change-Id: Ic5ddb051e5ac46f8dd56b26e2cb8ad8ad69c0d07
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7580176
Commit-Queue: Vidhan Jain <vidhanj@google.com>
Reviewed-by: Viktor Semeniuk <vsemeniuk@google.com>
Reviewed-by: Rainhard Findling <rainhard@chromium.org>
Reviewed-by: Rebekah Potter <rbpotter@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1587321}