UI Library configuration missing from feature branch

### Before opening, please confirm:

- [X] I have [searched for duplicate or closed issues](https://github.com/aws-amplify/amplify-adminui/issues?q=is%3Aissue+).
- [X] I have read the guide for [submitting bug reports](https://github.com/aws-amplify/amplify-adminui/blob/main/CONTRIBUTING.md#bug-reports).
- [X] I have done my best to include a minimal, self-contained set of instructions for consistently reproducing the issue.
- [X] I have removed any sensitive information from my code snippets and submission.

### App Id

d23hu3elmtkbzl

### Region

ap-southeast-2

### Environment name

multiple

### Figma File Version (if applicable)

_No response_

### Amplify CLI Version

10.4.1

### If applicable, what version of Node.js are you using?

_No response_

### What operating system are you using?

Windows

### Browser type?

Chrome

### Describe the bug

I'm trying to use the Feature Branch capability in Amplify Hosting to create separate backends for development purposes, but the UI Library configuration seems to be lost in the process.

I started out with a branch called staging, i did the initial setup in that environment including some figma components & UI library configuration to add slots, bindings, etc.

I've created a branch for a new feature, when i open Amplify Studio for the new environment the Figma file link is missing, and if i do a pull via the CLI all the generated UI components from my original branch get deleted.
I've tried reconnecting the figma file and it re-imports the components, but all the configuration done within the UI Library is missing (component slots, data binding, etc).

### Expected behavior

I would expect the figma file link and the configuration applied to individual components in the UI Library within the environment of a parent branch to be present in a new environment that was generated via a feature branch off the parent. If for some reason the figma file connection can't be passed through and needs to be re-authorized, i'd at least expect the individual component configuration not to be lost when the file is re-authorized, as that would be extremely time-consuming and error prone to re-create manually on every feature branch.

### Reproduction steps

1. Set up a project that includes components imported from figma
2. Link the project to a repo (Ours is in Bitbucket, though i wouldn't expect that to matter)
3. Apply manual configuration to the components via the UI Library page in Studio
4. Pull down the components via CLI & commit to the repo
5. Create a feature branch in the repo & use the 'Connect Branch' button in the AWS Amplify console homepage to create a new environment, including a new backend
6. Once the backend is deployed, open Amplify Studio and look at the UI Library

### Project Identifier

_No response_

### Additional information

_No response_

Start by reproducing the reported workflow in the AWS Amplify console: configure Figma components in the staging environment, create a connected feature branch, and inspect Amplify Studio's UI Library. Confirm whether the Figma link and component slots or data bindings persist after branching and CLI pull; done means the parent branch's UI Library configuration remains available in the new environment.

Written by the indexing model from the issue text.