Context lost when using Logback async appender

Describe the bug

When logging to an otel appender from an async appender, trace id and span id are missing.

Logging directly to the otel appender:

Trace ID: c19c9a3ae2dab1b1950e6073eddb5b8d
Span ID: 38035d648fa52857

Logging through the async appender:

Trace ID:
Span ID:

Steps to reproduce

    <appender name="otel-async" class="ch.qos.logback.classic.AsyncAppender">
        <appender-ref ref="otel-sync" />
    </appender>

    <appender name="otel-sync" class="io.opentelemetry.instrumentation.logback.appender.v1_0.OpenTelemetryAppender">
        <captureExperimentalAttributes>true</captureExperimentalAttributes>
        <captureMarkerAttribute>true</captureMarkerAttribute>
        <captureKeyValuePairAttributes>true</captureKeyValuePairAttributes>
    </appender>

    <root level="DEBUG">
        <appender-ref ref="otel-async"/>
    </root>

Expected behavior

Context would be propagated through the async appender to the otel appender so that trace and span ids would be included in log records.

Actual behavior

Trace and span ids are missing.

Javaagent or library instrumentation version

2.12.0

Environment

JDK: OpenJDK 21
OS: Ubuntu 23.10

Additional context

No response

Reproduce the issue with the provided Logback AsyncAppender and OpenTelemetryAppender configuration, then inspect how context is handled between those two appenders. Compare direct and asynchronous logging under OpenJDK 21. Done means trace and span IDs are present in records emitted through the async appender, with coverage for the reported configuration.