Issue when moving repo from Github to Bitbucket

### 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.

### App Id

d3snrzizftio23

### Region

eu-west-1

### Environment name

all envs

### Amplify CLI Version

5.3.1

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

16

### What operating system are you using?

Mac

### Browser type?

Brave (but tried accross Chrome/ Safari)

### Describe the bug

Hello 👋🏻

We previously had our Amplify project connected to a Github repo and then decided to move it to Bitbucket. The problem is that no matter how much we tried, when selecting a repo to connect, the Amplify console will just flash for a second pretending to load bitbucket, but then it will default to Github in a split second without allowing us to change it back.

We also tried doing it via CLI:
```
aws amplify update-app --app-id d3snrzizftio23 --repository https://bitbucket.org/eolas-medical/amplify-back-end --access-token XXXXXXXX
```
the problem here being on Bitbucket's end where they don't offer a singular access token (as Github do per example) and no matter what combination we tried, we couldn't make this change.

I think I've previously seen this exact problem raised around here but couldn't find the exact link.

Thanks!

### Expected behavior

I would expect that when going in the UI to change the repo, that will happen.

### Reproduction steps

1. Go https://eu-west-1.console.aws.amazon.com/amplify/home?region=eu-west-1#/d3snrzizftio23
2. Change repo to Bitbucket
3. It will automatically default to Github

### Additional information

_No response_

Start by reproducing the behavior in the AWS Amplify console using the listed app, region, and repository-change steps. Then inspect the `aws amplify update-app` path and the Bitbucket repository and access-token inputs; done means switching from GitHub to Bitbucket succeeds in the console and through the documented CLI flow.

Written by the indexing model from the issue text.