tRPC server errors not sent from vercel deployment. Local works fine

### 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?

Sentry Saas ([sentry.io]())

### Which SDK are you using?

@sentry/nextjs

### SDK Version

9.38.0

### Framework Version

15.4.1

### Link to Sentry event

*No response*

### Reproduction Example/SDK Setup

[https://github.com/studie-tech/TheNinjaRPG]()

I believe the most relevant files are:

```
https://github.com/studie-tech/TheNinjaRPG/blob/main/app/instrumentation.ts
https://github.com/studie-tech/TheNinjaRPG/blob/main/app/sentry.server.config.ts
https://github.com/studie-tech/TheNinjaRPG/blob/main/app/src/app/api/trpc/%5Btrpc%5D/route.ts
```

Specifically, I have implemented `Sentry.flush` as I thought that was the most likely culprit, but to no avail.

### Steps to Reproduce

Whenever I trigger an error in a tRPC endpoint on purpose, I get the error when working from local, but not when deployed on vercel. The full configuration can be seen here:
[studie-tech/TheNinjaRPG]()

I'm not using environment variables for the DSN, which seems to be a common cause of this. I've gone through the entire setup of Sentry again.

This worked a few months ago when initially set up, but has since then been broken.

### Expected Result

Expect similar behavior on local and vercel deployment

### Actual Result

No errors reported from vercel