FR (Authenticator): Ability to update formFIelds without remounting the Authenticator component

### On which framework/platform would you like to see this feature implemented?

React

### Which UI component is this feature-request for?

Authenticator

### Please describe your feature-request in detail.

Authenticator currently does not support changes to `formFIelds` after `Authenticator` has already initialized. Specifically, `` holds the formFields state, and needs to be remounted for your new `formfields` to take effect.

Parent component:
```jsx

```

MyApp:
```jsx

```
If you change userid after initially displaying the sign in page, it will not change. Moving Authenticator.Provider into MyApp is an acceptable workaround for now.

### Please describe a solution you'd like.

_No response_

### We love contributors! Is this something you'd be interested in working on?

- [ ] 👋 I may be able to implement this feature request.
- [ ] ⚠️ This feature might incur a breaking change.

Start with Authenticator.Provider and Authenticator, tracing how formFields are initialized and whether later prop changes are observed. Done means changing formFields, such as the sign-in username value or read-only state, takes effect without remounting either component.

Written by the indexing model from the issue text.