[APM Fix missing error.culprit (#205242)

fixes [#205240](https://github.com/elastic/kibana/issues/205240)

## Summary

Fixes the issue where `error.culprit` is always missing.

<img width="800" alt="image"
src="https://github.com/user-attachments/assets/9dad6797-dd40-4206-b508-daf8d69d653d"
/>

<img width="800" alt="image"
src="https://github.com/user-attachments/assets/6a0ac25a-bc4b-4a26-b126-86eecbe7e769"
/>



### How to test 

- Run `simple_trace` synthtrace scenario
- Run the request below
<details>
<summary>POST logs-apm.error-default/_doc</summary>

```
POST logs-apm.error-default/_doc
{

    "container": {
      "id": "80cc20ecab1b57865d7aca0f66ab75a0c6ec2c51f7c53da04a8540215369c359"
    },
    "kubernetes": {
      "node": {
        "name": "ip-192-168-55-136.ec2.internal"
      },
      "pod": {
        "uid": "9bbfe3dc-dace-4638-b8f5-aa6ccf435cbe",
        "name": "otel-demo-green-3-cartservice-5d5ccc86dd-gcxtr"
      },
      "namespace": "otel-demo-green-3"
    },
    "parent": {
      "id": "f39639f56a540e0e"
    },
    "agent": {
      "name": "opentelemetry/dotnet",
      "version": "1.6.0"
    },
    "source": {
      "port": 35136,
      "ip": "::ffff:192.168.50.132"
    },
    "error": {
      "exception": [
        {
          "handled": true,
          "message": "Exception (plain, .NET) without culprit",
          "type": "Grpc.Core.RpcException"
        }
      ],
      "culprit": "culprit msg", // remove to test the N/A scenario
      "id": "60674e9b23c8b06d83889e63ffe82c1c", //change the id on every run
      "stack_trace": "Grpc.Core.RpcException: Status(StatusCode=\"FailedPrecondition\", Detail=\"Can't access cart storage. System.ApplicationException: Wasn't able to connect to redis\n   at cartservice.cartstore.RedisCartStore.EnsureRedisConnected() in /usr/src/app/src/cartstore/RedisCartStore.cs:line 79\n   at cartservice.cartstore.RedisCartStore.EmptyCartAsync(String userId) in /usr/src/app/src/cartstore/RedisCartStore.cs:line 157\")\n   at cartservice.cartstore.RedisCartStore.EmptyCartAsync(String userId) in /usr/src/app/src/cartstore/RedisCartStore.cs:line 166\n   at cartservice.services.CartService.EmptyCart(EmptyCartRequest request, ServerCallContext context) in /usr/src/app/src/services/CartService.cs:line 65",
      "grouping_key": "6082c58afd7fa6838ebc27eef6e04829"
    },
    "message": "Exception (plain, .NET)",
    "url": {
      "path": "/oteldemo.CartService/EmptyCart",
      "original": "http://otel-demo-green-3-cartservice:8080/oteldemo.CartService/EmptyCart",
      "scheme": "http",
      "port": 8080,
      "domain": "otel-demo-green-3-cartservice",
      "full": "http://otel-demo-green-3-cartservice:8080/oteldemo.CartService/EmptyCart"
    },
    "labels": {
      "k8s_pod_ip": "192.168.62.174",
      "k8s_pod_start_time": "2024-12-17T02:55:54Z",
      "service_namespace": "opentelemetry-demo",
      "k8s_deployment_name": "otel-demo-green-3-cartservice"
    },
    "observer": {
      "hostname": "450fbf7ab701",
      "type": "apm-server",
      "version": "8.13.2"
    },
    "trace": {
      "id": "699f6d1039fc873191a1c983790db3a2"
    },
    "@timestamp": "2024-12-30T10:30:00.000Z",
    "data_stream": {
      "namespace": "default",
      "type": "logs",
      "dataset": "apm.error"
    },
    "service": {
      "node": {
        "name": "80cc20ecab1b57865d7aca0f66ab75a0c6ec2c51f7c53da04a8540215369c359"
      },
      "framework": {
        "name": "Microsoft.AspNetCore"
      },
       "name": "synth-node-0",
      "language": {
        "name": "dotnet"
      }
    },
    "host": {
      "hostname": "ip-192-168-55-136.ec2.internal",
      "name": "ip-192-168-55-136.ec2.internal"
    },
    "client": {
      "port": 35136,
      "ip": "::ffff:192.168.50.132"
    },
    "http": {
      "request": {
        "method": "POST"
      },
      "response": {
        "status_code": 200
      },
      "version": "2"
    },
    "event": {
      "agent_id_status": "missing",
      "ingested": "2024-12-18T18:04:22Z"
    },
    "transaction": {
      "id": "f39639f56a540e0e",
      "type": "request",
      "sampled": true
    },
    "user_agent": {
      "original": "grpc-go/1.59.0",
      "name": "Other",
      "device": {
        "name": "Other"
      }
    },
    "span": {
      "id": "f39639f56a540e0e"
    },
    "timestamp": {
      "us": 1704892605838000
    }
  }
```
</details>

x-pack/solutions/observability/plugins/apm/server/routes/errors/get_error_groups/get_error_sample_details.ts

@@ -13,6 +13,7 @@ import {
   AGENT_NAME,
   AGENT_VERSION,
   AT_TIMESTAMP,
+  ERROR_CULPRIT,
   ERROR_EXCEPTION,
   ERROR_GROUP_ID,
   ERROR_ID,
@@ -82,6 +83,7 @@ export async function getErrorSampleDetails({
     SPAN_ID,
     AGENT_VERSION,
     PROCESSOR_NAME,
+    ERROR_CULPRIT,
     ERROR_STACK_TRACE,
     ERROR_EXC_MESSAGE,
     ERROR_EXC_HANDLED,

x-pack/test/api_integration/deployment_agnostic/apis/observability/apm/mobile/errors/generate_data.ts

@@ -59,7 +59,11 @@ export async function generateData({
             .transaction({ transactionName: transaction.name })
             .errors(
               serviceGoProdInstance
-                .error({ message: `Error ${index}`, type: transaction.name })
+                .error({
+                  message: `Error ${index}`,
+                  type: transaction.name,
+                  culprit: `Error culprit ${index}`,
+                })
                 .timestamp(timestamp)
             )
             .duration(1000)

x-pack/test/api_integration/deployment_agnostic/apis/observability/apm/mobile/errors/group_id_samples.spec.ts

@@ -134,6 +134,10 @@ export default function ApiTest({ getService }: DeploymentAgnosticFtrProviderCon
               'Error 1'
             );
           });
+
+          it('displays correct error culprit info', () => {
+            expect(errorSampleDetailsResponse.error.error.culprit).to.equal('Error culprit 1');
+          });
         });
       });