psycopg2 instrumentation with cursor argument doesn't work

Environment
python3.10
opentelemetry-instrumentation-psycopg2: 0.35b2

Steps to reproduce

import psycopg2
import psycopg2.extras
import opentelemetry.instrumentation.psycopg2
from opentelemetry.exporter.otlp.proto.http.trace_exporter import OTLPSpanExporter
from opentelemetry import trace
from opentelemetry.sdk.resources import Resource
from opentelemetry.sdk.trace import TracerProvider, sampling
from opentelemetry.sdk.trace.export import BatchSpanProcessor


def main():
    tracer_provider = TracerProvider(
        sampler=sampling.ALWAYS_ON,
        resource=Resource.create(
            {
                "service.name": "test-postgresql-instrumentation",
                "service.version": "1.0.0",
            }
        ),
    )
    trace.set_tracer_provider(tracer_provider)

    tracer_provider.add_span_processor(
        BatchSpanProcessor(
            OTLPSpanExporter(
                endpoint="https://<url>/e/<id>/api/v2/otlp/v1/traces",
                headers={
                    "Authorization": "Api-Token <token>"
                },
            )
        )
    )
    tracer = trace.get_tracer("test-postgresql-instrumentation-tracer")

    opentelemetry.instrumentation.psycopg2.Psycopg2Instrumentor().instrument()

    cnx = psycopg2.connect(database="test_db_name")
    cursor = cnx.cursor(cursor_factory=psycopg2.extras.DictCursor)
    with tracer.start_as_current_span("main-test-span"):
        cursor.execute("SELECT * FROM test")
    cursor.close()
    cnx.close()


if __name__ == "__main__":
    main()

What is the expected behavior?
SELECT instrumentation record in main-test-span

What is the actual behavior?
No SELECT record

Additional context
This works (cursor_factory attribute moved to connect method):

import psycopg2
import psycopg2.extras
import opentelemetry.instrumentation.psycopg2
from opentelemetry.exporter.otlp.proto.http.trace_exporter import OTLPSpanExporter
from opentelemetry import trace
from opentelemetry.sdk.resources import Resource
from opentelemetry.sdk.trace import TracerProvider, sampling
from opentelemetry.sdk.trace.export import BatchSpanProcessor


def main():
    tracer_provider = TracerProvider(
        sampler=sampling.ALWAYS_ON,
        resource=Resource.create(
            {
                "service.name": "test-postgresql-instrumentation",
                "service.version": "1.0.0",
            }
        ),
    )
    trace.set_tracer_provider(tracer_provider)

    tracer_provider.add_span_processor(
        BatchSpanProcessor(
            OTLPSpanExporter(
                endpoint="https://<url>/e/<id>/api/v2/otlp/v1/traces",
                headers={
                    "Authorization": "Api-Token <token>"
                },
            )
        )
    )
    tracer = trace.get_tracer("test-postgresql-instrumentation-tracer")

    opentelemetry.instrumentation.psycopg2.Psycopg2Instrumentor().instrument()

    cnx = psycopg2.connect(database="test_db_name", cursor_factory=psycopg2.extras.DictCursor)
    cursor = cnx.cursor()
    with tracer.start_as_current_span("main-test-span"):
        cursor.execute("SELECT * FROM test")
    cursor.close()
    cnx.close()


if __name__ == "__main__":
    main()

Start at Psycopg2Instrumentor and trace how cursor_factory is handled when passed to cnx.cursor(), comparing it with the working connect(..., cursor_factory=...) case. Reproduce both examples, then verify that cursor.execute("SELECT * FROM test") creates a SELECT record inside main-test-span in each case.