Expecting exception when connecting to Sentry failed

### 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

### How do you use Sentry?

Self-hosted/on-premise

### Which SDK are you using?

@sentry/node

### SDK Version

10.19.0

### Framework Version

Node 22.20.0-alpine3.22 (Docker)

### Link to Sentry event

_No response_

### Reproduction Example/SDK Setup

```
import * as Sentry from '@sentry/node';
/* <...> */
try {
console.log('[DBG] sentry init starting...');
Sentry.init({
dsn: sentryDsn,
environment: globals.RELEASE_STAGE,
sendDefaultPii: true,
});
console.log('[DBG] sentry init finished...');

console.log('[DBG] sending typo fn:');
consolee.logg('[DBG] force sentry exception');

} catch (e) {
console.error('[DBG] console error: ', e)
Sentry.captureException(e);
};

```
### Steps to Reproduce

1. Created Docker image with node app, @sentry/node imported, Sentry init'ed
2. Launched it on a machine with wrong DNS settings (in my case, my self-hosted Sentry's DNS wasn't available in my nameserver)
3. Didn't get any errors in self-hosted Sentry

### Expected Result

Expected some exceptions during connecting or error pushing to self-hosted Sentry.

### Actual Result

No errors during Sentry.init() or Sentry.captureException().
When I fixed DNS settings, I've got tracked errors in Sentry dashboard.

### Additional Context

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Ready to provide more details.