Is there a way to read "dd" log properties from a different JSON path?

[gajus]

For context, we are using an opinionated logger, that only allows to inject dd in {"context":{"dd":{...}}}

Meanwhile, DataDog injects them to the top level object:

{
  context: {
    program: '@contra/contra-api',
    reqId: '488fb75c-873b-4f14-9026-69301a3bba9b',
    logLevel: 30,
    response: {
      statusCode: 200,
    },
    responseTime: 140.2810000181198
  },
  message: 'request completed',
  sequence: '10.11',
  time: 1648137086856,
  version: '2.0.0',
  dd: {
    trace_id: '3255415553032845221',
    span_id: '3255415553032845221',
    service: 'ts-node',
    version: '10.4.0'
  }
}

If left there, the resulting log message will be printed without dd:

{"context":{"reqId":"488fb75c-873b-4f14-9026-69301a3bba9b","program":"@contra/contra-api","logLevel":30,"responseTime":140.2810000181198,"response":{"statusCode":200}},"message":"request completed","sequence":"10.11","time":1648137086856,"version":"2.0.0"}

We could move it to context.dd and then the logs would get printed as expected:

{
    "context": {
        "dd": {
            "trace_id": "3255415553032845221",
            "span_id": "3255415553032845221",
            "service": "ts-node",
            "version": "10.4.0"
        },
        "reqId": "488fb75c-873b-4f14-9026-69301a3bba9b",
        "program": "@contra/contra-api",
        "logLevel": 30,
        "responseTime": 140.2810000181198,
        "response": {
            "statusCode": 200
        }
    },
    "message": "request completed",
    "sequence": "10.11",
    "time": 1648137086856,
    "version": "2.0.0"
}

Is there a way to configure datadog-agent to read dd context from there?