[Bug]: Upgrade - Version miss-match displayed in Chrome Extensions page and current MM version

### Describe the bug

After upgrading from 13.20.0 (browserify prod build) to 13.28.0 (browserify RC build) I see that the Chrome extension page displays briefly the correct 13.28 version but then it displayed the incorrect older version of MM.
If I go to Settings I do see 13.28.0 but on the Extension page I see the incorrect version.

### Expected behavior

_No response_

### Screenshots/Recordings

https://github.com/user-attachments/assets/dba92e45-f04f-4109-a674-ab29c1d9a68e

### Steps to reproduce

1. Have installed a prod build in your browser
2. Go to chrome://extensions page
3. Click Load unpack
4. Upload the 13.28.0 browserify RC build
5. See how MM upgrades
6. Go to settings
7. See the correct version there
8. See incorrect version in chrome:/extensions no matter if you refresh or reload

### Error messages or log output

```shell

```

### Where was this bug found?

Internal release testing

### Version

13.28.0

### Build type

None

### Browser

Chrome

### Operating system

MacOS

### Hardware wallet

_No response_

### Additional context

_No response_

### Severity

_No response_

[Jira issue](https://consensyssoftware.atlassian.net/browse/MCTP-198)

### Expected behavior

No response

### Screenshots/Recordings

No response

### Steps to reproduce

1. Have installed a prod build in your browser
2. Go to chrome://extensions page
3. Click Load unpack
4. Upload the 13.28.0 browserify RC build
5. See how MM upgrades
6. Go to settings
7. See the correct version there
8. See incorrect version in chrome:/extensions no matter if you refresh or reload

### Error messages or log output

```shell

```

### Where was this bug found?

No response

### Version

13.28.0

### Build number

No response

### Build type

None

### Browser

Chrome

### Operating system

MacOS

### Hardware wallet

No response

### Additional context

No response

### Severity

Sev2

Start by reproducing the upgrade from the 13.20.0 browserify production build to the 13.28.0 browserify RC build, then compare the version shown in Settings with chrome://extensions. Trace where each page obtains its version and verify that both display 13.28.0 after loading, refreshing, and reloading the extension.

Written by the indexing model from the issue text.