[DBMON-6787] Remove duplicated agent_hostname logic from postgres (#24270)

* [DBMON-6787] Remove duplicated agent_hostname logic from postgres

Co-authored-by: Cursor <cursoragent@cursor.com>

* Add changelog

Co-authored-by: Cursor <cursoragent@cursor.com>

---------

Co-authored-by: Cursor <cursoragent@cursor.com>

Author: eric-weaver

postgres/changelog.d/24270.fixed

@@ -0,0 +1 @@
+Remove duplicated agent_hostname logic now provided by the DatabaseCheck base class.

postgres/datadog_checks/postgres/postgres.py

@@ -121,7 +121,6 @@ def __init__(self, name, init_config, instances):
         self.health = PostgresHealth(self)
         self._resolved_hostname = None
         self._database_identifier = None
-        self._agent_hostname = None
         self._database_hostname = None
         self._db = None
         self._cloud_metadata: dict[str, dict] = None
@@ -737,13 +736,6 @@ def set_resolved_hostname_metadata(self):
         """
         self.set_metadata('resolved_hostname', self._resolved_hostname)
 
-    @property
-    def agent_hostname(self):
-        # type: () -> str
-        if self._agent_hostname is None:
-            self._agent_hostname = datadog_agent.get_hostname()
-        return self._agent_hostname
-
     @property
     def database_hostname(self):
         # type: () -> str