Not all exceptions are populated with exception type and message

Expected behavior

Span should contain exception type and message. More details: https://github.com/microsoft/ApplicationInsights-Java/pull/3148

Actual behavior

Exception type and message is not added in case exception is not propagated to main thread. Span will contain only exception field.

In other cases span contains exception.type and excpetion.message, without exception field.

Looks like inconsistent behavior which produces completely different fields.

To Reproduce

Code:

BlobServiceClient blobServiceClient = ...
BlobContainerClient blobContainerClient = blobServiceClient.getBlobContainerClient("blob-name");
blobContainerClient.exists();

Exception is not thrown to main thread, but rather caught inside blobContainerClient.exists().

Produced span:

2024-06-11 12:18:58.916+03:00 DEBUG c.m.a.a.i.exporter.AgentSpanExporter - exporting span: SpanData{
    spanContext=ImmutableSpanContext{traceId=REDACTED, spanId=REDACTED, traceFlags=01, traceState=ArrayBasedTraceState{entries=[]}, remote=false, valid=true}, 
    parentSpanContext=ImmutableSpanContext{traceId=REDACTED, spanId=REDACTED, traceFlags=01, traceState=ArrayBasedTraceState{entries=[]}, 
    remote=false, valid=true}, resource=Resource{schemaUrl=null, attributes={service.name="unknown_service:java", telemetry.sdk.language="java", telemetry.sdk.name="opentelemetry", telemetry.sdk.version="1.35.0"}}, 
    instrumentationScopeInfo=InstrumentationScopeInfo{name=azure-storage-blob, version=12.25.3, schemaUrl=https://opentelemetry.io/schemas/1.17.0, attributes={}}, 
    name=AzureBlobStorageCont.getProperties, kind=INTERNAL, startEpochNanos=1718097538120247437, endEpochNanos=1718097538844404395, 
    attributes=AttributesMap{data={az.namespace=Microsoft.Storage, thread.id=70, applicationinsights.internal.operation_name=REDACTED, thread.name=http-nio-8080-exec-1}, capacity=128, totalAddedValues=4}, 
    totalAttributeCount=4, events=[ImmutableExceptionEventData{epochNanos=1718097538844385117, exception=com.azure.storage.blob.models.BlobStorageException: Status code 404, "<?xml version="1.0" encoding="utf-8"?><Error><Code>ContainerNotFound</Code><Message>The specified container does not exist.

RequestId:REDACTED
Time:2024-06-11T09:18:58.7592080Z</Message></Error>", additionalAttributes={}, spanLimits=SpanLimitsValue{maxNumberOfAttributes=128, maxNumberOfEvents=128, maxNumberOfLinks=128, maxNumberOfAttributesPerEvent=128, maxNumberOfAttributesPerLink=128, maxAttributeValueLength=2147483647}}], totalRecordedEvents=1, links=[], totalRecordedLinks=0, status=ImmutableStatusData{statusCode=ERROR, description=}, hasEnded=true}