[Next.js] Support Bun & Railpack

### Is there an existing issue for this?

- [x] I have checked for existing issues https://github.com/getsentry/sentry-javascript/issues
- [x] I have reviewed the documentation https://docs.sentry.io/
- [x] I am using the latest SDK release https://github.com/getsentry/sentry-javascript/releases

Prior discussion on Discord: https://discord.com/channels/621778831602221064/1351742239360942171

### How do you use Sentry?

Self-hosted/on-premise

### Which SDK are you using?

@sentry/nextjs

### SDK Version

8.55.0

### Framework Version

15.2.2

### Link to Sentry event

_No response_

### Reproduction Example/SDK Setup

_No response_

### Steps to Reproduce

- Use `bun install` instead of npm/pnpm/yarn
- Get error while compiling (in CI)

### Expected Result

- use `bun install`
- Deployment finished successfully

### Actual Result

- use `bun install`
- Deployments fails with `sentry reported an error: Invalid org token (http status: 401)`