opentelemetry-instrumentation-logging JSON Formatter compatibility with spec

The spec for log formatting, specifically JSON has an example:

https://opentelemetry.io/docs/specs/otel/compatibility/logging_trace_context/#json-formats

Which seems to reinforce the overview of logging Trace ID and Span ID in legacy log formats:

To summarize, the following field names should be used in legacy formats:

“trace_id” for TraceId, lowercase and hex-encoded.
“span_id” for SpanId, lowercase and hex-encoded.
“trace_flags” for trace flags, formatted according to W3C traceflags format.

However, the log record that is created with the opentelemetry-instrumentation-logging has fields named otelTraceID and otelSpanID, etc.:

https://github.com/open-telemetry/opentelemetry-python-contrib/blob/26c975f2aea142ef198c1a4b377d7cb71bbbbd57/instrumentation/opentelemetry-instrumentation-logging/src/opentelemetry/instrumentation/logging/__init__.py#L203-L205

This doesn't rear it's head with standard text formatters as the default logging format pulls the appropriate log record attributes out explicitly: https://github.com/open-telemetry/opentelemetry-python-contrib/blob/26c975f2aea142ef198c1a4b377d7cb71bbbbd57/instrumentation/opentelemetry-instrumentation-logging/src/opentelemetry/instrumentation/logging/constants.py#L4

JSON formatters traditionally just take what they are given and spit them out, see reference implementation: python-json-logger.

I believe the attributes placed onto the log record should change to snake case, and the default text format changed to leverage them appropriately.

Start in instrumentation/opentelemetry-instrumentation-logging/src/opentelemetry/instrumentation/logging/init.py around the log-record attributes and in constants.py around the default text format. Compare those names and formatting rules with the linked OpenTelemetry JSON specification and python-json-logger behavior. Done means the instrumentation is compatible with the specified JSON field names while the default text format still emits the expected values.