traced_execution_async` in `opentelemetry-instrumentation-dbapi` ignores instrumentation suppression

Describe your environment

• opentelemetry-instrumentation-dbapi 0.62b1
• opentelemetry-instrumentation-psycopg 0.62b1
• psycopg 3 with AsyncConnection / AsyncConnectionPool
• Python 3.14

What happened?

Spans are still created (and exported) for queries executed inside
opentelemetry.instrumentation.utils.suppress_instrumentation() when the
cursor is async. The sync path correctly suppresses.

Steps to Reproduce

from opentelemetry.instrumentation.psycopg import PsycopgInstrumentor
from opentelemetry.instrumentation.utils import suppress_instrumentation
from opentelemetry.sdk.trace import TracerProvider
from opentelemetry.sdk.trace.export import SimpleSpanProcessor
from opentelemetry.sdk.trace.export.in_memory_span_exporter import InMemorySpanExporter

from psycopg import AsyncConnection

exporter = InMemorySpanExporter()
provider = TracerProvider()
provider.add_span_processor(SimpleSpanProcessor(exporter))
PsycopgInstrumentor().instrument(tracer_provider=provider)

async def main():
    async with await AsyncConnection.connect(DSN) as conn:
        async with conn.cursor() as cur:
            with suppress_instrumentation():
                await cur.execute("SELECT 1")

# after running main():
assert exporter.get_finished_spans() == ()   # FAILS — one span was exported

The same code with a sync psycopg.connect() passes.

Expected Result

No span — the async path should honor suppression exactly as the sync path
does.

Actual Result

One span was created and exported for the SELECT 1 executed inside suppress_instrumentation() — exporter.get_finished_spans() returns a span named SELECT with db.statement = "SELECT 1", and the final assertion in the reproducer fails.
Running the identical code with a sync psycopg.connect() connection produces no span — the sync path honors suppression, the async path does not.

Additional context

The common use of suppress_instrumentation() around background polls
(outbox sweeps, health/metric COUNT queries) silently stops working the day a
codebase migrates from sync to async connections — every poll becomes a root
span again, with no error and no signal that suppression is inert. Tests that
assert is_instrumentation_enabled() inside the block keep passing, because
the flag is set correctly; it is simply never read.

Would you like to implement a fix?

None

Tip

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Start in the opentelemetry-instrumentation-dbapi async cursor execution path and compare it with the sync path, using the provided psycopg AsyncConnection reproducer. Verify the change by checking that the suppression block produces no finished spans, while the existing sync behavior remains unchanged.