[Bug]: Initialization - `The executor for "npm:@metamask/message-signing-snap" failed to initialize`

### Describe the bug

This error has been captured in our e2e tests right after login into the wallet.
I can see how the Bitcoin account is not in the wallet (the Solana one is there).

`The executor for "npm:@metamask/message-signing-snap" failed to initialize`
After:

`Error: Unable to enable notifications.`

### Expected behavior

No error, and non-EVM accounts loaded

### Screenshots/Recordings

### Steps to reproduce

This has been captured by chance in one of our e2e tests.
Sharing here the logs for further investigation: https://github.com/MetaMask/metamask-extension/actions/runs/26493009696/job/78015762838

The failure is not consistent, so it's hard to reproduce

### Error messages or log output

```shell

```

### Where was this bug found?

Internal release testing

### Version

main

### Build type

None

### Browser

Chrome

### Operating system

MacOS

### Hardware wallet

_No response_

### Additional context

_No response_

### Severity

_No response_

Start with the linked e2e job logs and trace the login flow around the notification error and message-signing Snap initialization. Compare the cases where the Bitcoin account is absent with successful runs, then identify the initialization failure and verify that login completes without errors and non-EVM accounts load.

Written by the indexing model from the issue text.