Handle TimeoutError on sending message to Slack (#4916)

# What this PR does

## Which issue(s) this PR closes

Related to https://github.com/grafana/oncall-private/issues/2758

<!--
*Note*: If you want the issue to be auto-closed once the PR is merged,
change "Related to" to "Closes" in the line above.
If you have more than one GitHub issue that this PR closes, be sure to
preface
each issue link with a [closing
keyword](https://docs.github.com/en/get-started/writing-on-github/working-with-advanced-formatting/using-keywords-in-issues-and-pull-requests#linking-a-pull-request-to-an-issue).
This ensures that the issue(s) are auto-closed once the PR has been
merged.
-->

## Checklist

- [x] Unit, integration, and e2e (if applicable) tests updated
- [x] Documentation added (or `pr:no public docs` PR label added if not
required)
- [x] Added the relevant release notes label (see labels prefixed w/
`release:`). These labels dictate how your PR will
    show up in the autogenerated release notes.

engine/apps/slack/scenarios/distribute_alerts.py

@@ -73,7 +73,7 @@ class AlertShootingStep(scenario_step.ScenarioStep):
                     else alert.group.channel.organization.general_log_channel_id
                 )
                 self._send_first_alert(alert, channel_id)
-            except SlackAPIError:
+            except (SlackAPIError, TimeoutError):
                 AlertGroup.objects.filter(pk=alert.group.pk).update(slack_message_sent=False)
                 raise
 

engine/apps/slack/tests/test_scenario_steps/test_distribute_alerts.py

@@ -39,6 +39,38 @@ def test_restricted_action_error(
     assert not alert.delivered
 
 
+@pytest.mark.django_db
+def test_timeout_error(
+    make_slack_team_identity,
+    make_organization,
+    make_alert_receive_channel,
+    make_alert_group,
+    make_alert,
+):
+    SlackAlertShootingStep = ScenarioStep.get_step("distribute_alerts", "AlertShootingStep")
+    slack_team_identity = make_slack_team_identity()
+    organization = make_organization(
+        slack_team_identity=slack_team_identity, general_log_channel_id="DEFAULT_CHANNEL_ID"
+    )
+    alert_receive_channel = make_alert_receive_channel(organization)
+    alert_group = make_alert_group(alert_receive_channel)
+    alert = make_alert(alert_group, raw_request_data="{}")
+
+    step = SlackAlertShootingStep(slack_team_identity)
+
+    with pytest.raises(TimeoutError):
+        with patch.object(step._slack_client, "api_call") as mock_slack_api_call:
+            mock_slack_api_call.side_effect = TimeoutError
+            step.process_signal(alert)
+
+    alert_group.refresh_from_db()
+    alert.refresh_from_db()
+    assert alert_group.slack_message is None
+    assert alert_group.slack_message_sent is False
+    assert SlackMessage.objects.count() == 0
+    assert not alert.delivered
+
+
 @patch.object(AlertShootingStep, "_post_alert_group_to_slack")
 @pytest.mark.django_db
 def test_alert_shooting_no_channel_filter(