Query Wait Timout Error from Pgbouncer Not Propogating to Client

Reproduce the timeout through the pgbouncer setup described in the issue, then start at asyncpg/connection.py's Connection.execute path and asyncpg/protocol/protocol.pyx query. Compare the error handling with the psycopg and psql examples, and verify that the client exposes the query_wait_timeout error rather than only reporting a closed connection.

When pgbouncer kills a connection due to its query_wait_timeout, the error message is not propagated to the client. All that is provided to the client is a not very helpful message "connection was closed in the middle of operation". This error message seems to be correctly handled by psql and psycopg.

I replicated this by using a pgbouncer instance with a pool_size of 1 and made sure another connection was consuming this connection to ensure that the connection would be put in a waiting mode.

asyncpg version

 > python -c 'import asyncpg; print(asyncpg.__version__)'
0.31.0

Example asyncpg code

import asyncio
import asyncpg

async def main():
    conn = await asyncpg.connect('postgresql://postgres@localhost:6432/postgres')
    row = await conn.execute('SELECT 1')

asyncio.run(main())

Stdout from the above code

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib/python3.12/asyncio/runners.py", line 194, in run
    return runner.run(main)
           ^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/asyncio/runners.py", line 118, in run
    return self._loop.run_until_complete(task)
           ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/usr/lib/python3.12/asyncio/base_events.py", line 687, in run_until_complete
    return future.result()
           ^^^^^^^^^^^^^^^
  File "<stdin>", line 3, in main
  File "/path/to/venv/lib/python3.12/site-packages/asyncpg/connection.py", line 349, in execute
    result = await self._protocol.query(query, timeout)
             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "asyncpg/protocol/protocol.pyx", line 375, in query
asyncpg.exceptions.ConnectionDoesNotExistError: connection was closed in the middle of operation

Example code for psycopg

import psycopg
with psycopg.connect("postgresql://postgres:@localhost:6432/postgres") as conn:
    with conn.cursor() as cur:
         cur.execute("SELECT 1")

example traceback from psycopg

Traceback (most recent call last):
  File "<stdin>", line 3, in <module>
  File "/path/to/venv/lib/python3.12/site-packages/psycopg/cursor.py", line 97, in execute
    raise ex.with_traceback(None)
psycopg.errors.ProtocolViolation: query_wait_timeout

Example call and stdout from psql on query_wait_timeout

> psql \
    'postgresql://postgres:@localhost:6432/postgres' \
    --command='SELECT 1'

FATAL:  query_wait_timeout
server closed the connection unexpectedly
        This probably means the server terminated abnormally
        before or while processing the request.
connection to server was lost