Postgres integration fails to submit postgres.can_connect failure for database when connection is refused on network level in Azure

[anordby]

Trace log from datadog event:

2023-12-13 12:06:41 CET | CORE | TRACE | (pkg/collector/runner/expvars/expvars.go:129 in AddCheckStats) | Adding stats for postgres:63f61c8625e257c8
2023-12-13 12:06:41 CET | CORE | DEBUG | (pkg/collector/worker/check_logger.go:60 in CheckFinished) | check:postgres | Done running check
2023-12-13 12:06:42 CET | CORE | TRACE | (pkg/collector/scheduler/job.go:181 in process) | Bucket ticked... current index: 0
2023-12-13 12:06:42 CET | CORE | TRACE | (pkg/collector/scheduler/job.go:197 in process) | Jobs in bucket: [disk]
2023-12-13 12:06:42 CET | CORE | DEBUG | (pkg/collector/worker/check_logger.go:43 in CheckStarted) | check:disk | Running check...

Environment: Debian Linux Stretch 64 bit, Azure VM. Running datadog agent 7.49.1

Steps to reproduce the issue:

1. Install datadog agent and set up (successful) monitoring of Postgres database with Azure managed "Azure Database for PostgreSQL servers"
2. Close connectivity to Azure PostgreSQL server by: removing all vnet openings, set deny public access etc so that database is unreachable.
3. Check Datadog agent trace log and DataDog monitor of PostgreSQL integration status postgres.can_connect, result for your databse will not be there while a connection failure is expected

Expected result: expect a failure on the postgresql.can_connect result, similar to what happens here on another VM where credentials are wrong:

023-12-13 11:15:16 UTC | CORE | ERROR | (pkg/collector/python/datadog_agent.go:129 in LogMessage) | postgres:8d9a572b38a26f09 | (postgres.py:764) | Unable to collect postgres metrics.
Traceback (most recent call last):
  File "/opt/datadog-agent/embedded/lib/python3.9/site-packages/datadog_checks/postgres/postgres.py", line 744, in check    self._connect()
  File "/opt/datadog-agent/embedded/lib/python3.9/site-packages/datadog_checks/postgres/postgres.py", line 573, in _connect
    self.db = self._new_connection(self._config.dbname)
  File "/opt/datadog-agent/embedded/lib/python3.9/site-packages/datadog_checks/postgres/postgres.py", line 557, in _new_connection
    conn = psycopg2.connect(**args)
  File "/opt/datadog-agent/embedded/lib/python3.9/site-packages/psycopg2/__init__.py", line 127, in connect
    conn = _connect(dsn, connection_factory=connection_factory, **kwasync)
psycopg2.OperationalError: FATAL:  password authentication failed for user "datadog"
2023-12-13 11:15:16 UTC | CORE | DEBUG | (pkg/collector/python/datadog_agent.go:135 in LogMessage) | postgres:8d9a572b38a26f09 | (postgres.py:223) | Cleaning state
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/collector/python/memory.go:76 in MemoryTracker) | Memory Tracker - ptr: 0x7f71d007a4d0, sz: 56, op: 0
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/collector/python/memory.go:76 in MemoryTracker) | Memory Tracker - ptr: 0x7f71d003b640, sz: 28, op: 0
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/collector/python/memory.go:76 in MemoryTracker) | Memory Tracker - ptr: 0x7f71d0047540, sz: 11, op: 0
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/collector/python/memory.go:76 in MemoryTracker) | Memory Tracker - ptr: 0x7f71d0023d10, sz: 37, op: 0
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/collector/python/memory.go:76 in MemoryTracker) | Memory Tracker - ptr: 0x7f71d003ceb0, sz: 10, op: 0
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/collector/python/memory.go:76 in MemoryTracker) | Memory Tracker - ptr: 0x7f71d003d050, sz: 16, op: 0
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/collector/python/memory.go:76 in MemoryTracker) | Memory Tracker - ptr: 0x7f71d0094a20, sz: 99, op: 0
2023-12-13 11:15:16 UTC | CORE | TRACE | (pkg/aggregator/sender.go:346 in ServiceCheck) | Service check submitted:  postgres.can_connect :  CRITICAL  for hostname:  jumpbox.4rvjf015rjdurjvumtkvfmayzh.ax.internal.cloudapp.net  tags:  [pghost:moller-db0-prod-pgdb pgenv:prod server:db0-prod-pgdb.local.moller.no port:5432 db:smaxint_prod dd.internal.resource:database_instance:jumpbox.4rvjf015rjdurjvumtkvfmayzh.ax.internal.cloudapp.net]

Happens all the time.