TimeoutError on multiple requests

• asyncpg version: 0.27.0
• PostgreSQL version: 14.7
• Do you use a PostgreSQL SaaS? If so, which? Can you reproduce
  the issue with a local PostgreSQL install?: We can reproduce it, not locally
• Python version: 3.10.2
• Platform: Backend: Linux, t3large AWS instance, Database: AWS RDS
• Do you use pgbouncer?: No
• Did you install asyncpg with pip?: Yes

We're using FastAPI ,and our current code for setting up the db connection is:

connection_arguments: Dict[str, Any] = {"server_settings": {"jit": "off"}}

ENUM_TYPES = (
    ("public", "sometype"), ...
)

async def register_enum_types(conn) -> None: 
    for enum_class, typename in ENUM_TYPES:
        await conn.set_builtin_type_codec(
            typename, schema=enum_class, codec_name="text"
        )


engine = create_async_engine(
    settings.uri,
    echo=False,
    connect_args=connection_arguments,
    pool_size=200,
    max_overflow=10,
)

async_sessionmaker = sessionmaker(engine, class_=AsyncSession, expire_on_commit=False)


@event.listens_for(engine.sync_engine, "connect")
def on_connect(dbapi_connection, connection_record):
    dbapi_connection.run_async(register_enum_types)

We added the register_enum_types as we were thinking that the query:
SELECT t.oid, t.typelem AS elemtype, t.typtype AS kind FROM pg_catalog.pg_type AS t WHERE t.oid = $1

which we saw a lot in AWS RDS monitoring is causing the issue, but now we're not sure what is it anymore.

In logs when it happens we see:

File "/path/to/file/python3.10/site-packages/asyncpg/connect_utils.py", line 780, in _connect_addr raise asyncio.TimeoutError asyncio.exceptions.TimeoutError

and after some time, it gets back to normal.

Comience en asyncpg/connect_utils.py:780, donde se produce el asyncio.TimeoutError reportado, y revise el establecimiento de la conexión usando FastAPI, el pooling de SQLAlchemy y AWS RDS. Compare los registros de timeout con la configuración del pool concurrente y la consulta pg_catalog reportada. Se considerará terminado cuando se haya establecido una causa reproducible y un fix verificado o un diagnóstico claro.