Logback sdk install does not work for async appenders

[ataraxis]

Describe the bug

OpenTelemetryAppender.install iterates through all the loggers to find appenders where it should inject the sdk. When using an async appender though, OpenTelemetryAppender is referenced through the async appender rather than directly from a logger so the sdk does not get installed.

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

Appender references would be traversed recursively and the sdk installed on appenders that are only referenced from other appenders.

Actual behavior

Only appenders referenced directly from a logger are iterated. The following can workaround the issue, but it's non-obvious.

    <logger name="dummy" level="OFF">
      <appender-ref ref="otel-sync" />
    </logger>

Javaagent or library instrumentation version

2.11

Environment

JDK: 17
OS: Ubuntu 23.10

Additional context

No response