BUG: Overlapping application validation is logged as an unhandled exception

**Describe the Bug**

Submitting an application with overlapping study dates or a pending program information request returns 422 and is emitted as an unhandled exception.

**Expected Behaviour**

The known application validation is presented as an expected client response and does not generate a misleading unhandled-exception error log.

**Actual Behaviour**

`submitApplication` throws `UnprocessableEntityException`, which `AppAllExceptionsFilter` records as unhandled.

**Related Issues**

#4203 and #5651 discuss overlap validation behavior. This report captures the production logging behavior.

**Log**

```text
[Nest] 18 - 09/04/2026, 6:22:12 AM LOG [AccessLoggerMiddleware] Request - PATCH /api/students/application/[redacted]/submit From [redacted] | User GUID: [redacted] | User Agent: Chrome 152 on Windows
[Nest] 18 - 09/04/2026, 6:22:13 AM ERROR [AppAllExceptionsFilter] Unhandled exception, request path: /api/students/application/[redacted]/submit
{
"stack": "UnprocessableEntityException: There is an existing application already with overlapping study dates or a pending program information request. Please contact your institution for further assistance.\n at ApplicationStudentsController.submitApplication (webpack://studentaid-backend/apps/api/src/route-controllers/application/application.students.controller.ts:292:19)",
"status": 422,
"message": "There is an existing application already with overlapping study dates or a pending program information request. Please contact your institution for further assistance.",
"name": "UnprocessableEntityException"
}
```

Start in apps/api/src/route-controllers/application/application.students.controller.ts at submitApplication and trace how its UnprocessableEntityException reaches AppAllExceptionsFilter. Review how known application validation responses are classified, then verify that the 422 response remains unchanged while the overlap or pending-request case is no longer logged as an unhandled exception.

Written by the indexing model from the issue text.