Nextjs server-side calls to Rollbar not working

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- [X] I have checked to see if my question is addressed in the [FAQ](https://github.com/aws-amplify/amplify-hosting/blob/master/FAQ.md).
- [X] I have [searched for duplicate or closed issues](https://github.com/aws-amplify/amplify-hosting/issues?q=is%3Aissue+).
- [X] I have read the guide for [submitting bug reports](https://github.com/aws-amplify/amplify-hosting/blob/master/CONTRIBUTING.md).
- [X] I have done my best to include a minimal, self-contained set of instructions for consistently reproducing the issue.

### App Id

dfbnpz3ic6vce

### Region

us-east-1

### Amplify Hosting feature

Not applicable

### Describe the bug

Our Next.js application uses Rollbar for error monitoring. Errors/API calls originating from the browser work fine, but server-side errors triggered in `getServerSideProps` and API routes just never make it to Rollbar for some reason. I assume this is also the case for `getStaticProps`.

I have verified the environment variable used for the access token is there, and am able to log the same information to the console.

The exact same code works when run locally.

This is probably a separate issue, but errors thrown in `getServerSideProps` are also not passing the error through to `_error.js`, i.e. `ctx.err` is just empty.

### Expected behavior

Calls to Rollbar should work both client and server-side.

### Reproduction steps

1. Create Next.js app
2. `npm install rollbar`
3. Create API route that calls `rollbar.error()`
4. `npm run build`
5. `npm start`
6. Visit API route
7. Works
8. Deploy to Amplify
9. Visit same API route
10. Doesn't work

Example repo here: https://github.com/pjaws/amplify-next-rollbar

### Build Settings

_No response_

### Additional information

Error logged from local server in example repo:

Error logged to console in Amplify deployment:

Start with the linked example repository and reproduce the behavior using the API route, getServerSideProps, and the documented npm build/start deployment steps. Compare the local server logs with the Amplify deployment logs and verify whether server-side Rollbar calls reach Rollbar after deployment; also check the reported _error.js behavior.

Written by the indexing model from the issue text.