Turbopack instrumentation fails with permission denied error on CI

### 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

9.14.0

### Framework Version

Next 15.3.0

### Link to Sentry event

_No response_

### Reproduction Example/SDK Setup

https://github.com/wladpaiva/sentry-gh-error

### Steps to Reproduce

1. add a file to the root of the project that sentry wont have permissions
2. run nextjs on CI

### Expected Result

No error at all

### Actual Result

Getting [this](https://github.com/wladpaiva/sentry-gh-error/actions/runs/14629634922/job/41049218132#step:8:5) error of permissions denied when running a nextjs with playwright on CI ever since I updated sentry package from 9.6.0 to 9.13.0. Tried the 9.14 but same issue.

```
Run npx playwright test
npx playwright test
shell: /usr/bin/bash -e {0}

[WebServer] [Error [TurbopackInternalError]: [project]/node_modules/@sentry/nextjs/build/cjs/config/withSentryConfig.js [instrumentation] (ecmascript)
[WebServer]
[WebServer] Caused by:
[WebServer] - reading dir /home/runner/work/sentry-gh-error/sentry-gh-error/docker-data/postgres
[WebServer] - Permission denied (os error 13)
[WebServer]
[WebServer] Debug info:
[WebServer] - Execution of TaskId { id: [2](https://github.com/wladpaiva/sentry-gh-error/actions/runs/14629634922/job/41049218132#step:8:2)147483652 } transient failed
[WebServer] - Execution of get_written_endpoint_with_issues_operation failed
[WebServer] - Execution of endpoint_write_to_disk failed
[WebServer] - Execution of ::output failed
[WebServer] - Execution of InstrumentationEndpoint::output_assets failed
[WebServer] - Execution of InstrumentationEndpoint::node_chunk failed
[WebServer] - Execution of ModuleGraph::from_entry_module failed
[WebServer] - Execution of SingleModuleGraph::new_with_entries failed
[WebServer] - [project]/node_modules/@sentry/nextjs/build/cjs/config/withSentryConfig.js [instrumentation] (ecmascript)
[WebServer] - Execution of primary_chunkable_referenced_modules failed
[WebServer] - Execution of resolve_reference_from_dir failed
[WebServer] - Execution of read_matches failed
[WebServer] - Execution of read_matches failed
[WebServer] - Execution of read_matches failed
[WebServer] - Execution of read_matches failed
[WebServer] - Execution of ::raw_read_dir failed
[WebServer] - reading dir /home/runner/work/sentry-gh-error/sentry-gh-error/docker-data/postgres
[WebServer] - Permission denied (os error 1[3](https://github.com/wladpaiva/sentry-gh-error/actions/runs/14629634922/job/41049218132#step:8:3))]
Error: Process from config.webServer exited early.
Error: Process completed with exit code 1.
```