Execution API set_xcom endpoint returns non-RFC 9457 error for invalid value

### Under which category would you file this issue?

Airflow Core

### Apache Airflow version

main

### What happened and how to reproduce it?

**Issue Description**
In the Task Execution API, when a worker attempts to set an XCom via the `set_xcom` endpoint and the underlying `XComModel.set()` raises a `ValueError` (for example, if the DAG run or task instance cannot be resolved), the API currently rejects the request and raises an `HTTPException` with a `404 Not Found` status.

However, the `detail` returned is just the raw exception string:
`raise HTTPException(status.HTTP_404_NOT_FOUND, str(e))`

This violates the Airflow RFC 9457 error response requirements for the Execution API, which mandate that domain-layer exceptions should be caught and returned as structured detail schemas (e.g., `{"reason": "...", "message": "..."}`).

**Steps to reproduce:**
1. Send a POST request to `/execution/xcoms/{dag_id}/{run_id}/{task_id}/{key}` with parameters that cause `XComModel.set()` to raise a `ValueError`.
2. Observe the 404 response payload format and see that it is just a plain string instead of a valid RFC 9457 dictionary.

### What you think should happen instead?

The exception handler should return an RFC 9457 compliant detail dictionary, for example:

```python
raise HTTPException(
status_code=status.HTTP_404_NOT_FOUND,
detail={"reason": "not_found", "message": str(e)},
)
```

### Operating System

Not Applicable

### Deployment

None

### Apache Airflow Provider(s)

_No response_

### Versions of Apache Airflow Providers

_No response_

### Official Helm Chart version

Not Applicable

### Kubernetes Version

Not Applicable

### Helm Chart configuration

Not Applicable

### Docker Image customizations

Not Applicable

### Anything else?

_No response_

### Are you willing to submit PR?

- [x] Yes I am willing to submit a PR!

### Code of Conduct

- [x] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

Start at the Task Execution API set_xcom endpoint and trace how ValueError from XComModel.set() is converted into the 404 response. Confirm the response detail is an RFC 9457-compatible dictionary containing reason and message, and reproduce the invalid DAG run or task instance case to verify the payload.

Written by the indexing model from the issue text.