Fix integration test teardown error

If you don't close DB connections when you're done with them, I will scream

cylc/flow/dbstatecheck.py

@@ -72,7 +72,7 @@ def __init__(self, rund, workflow, db_path=None):
         if not os.path.exists(db_path):
             raise OSError(errno.ENOENT, os.strerror(errno.ENOENT), db_path)
 
-        self.conn = sqlite3.connect(db_path, timeout=10.0)
+        self.conn: sqlite3.Connection = sqlite3.connect(db_path, timeout=10.0)
 
         # Get workflow point format.
         try:
@@ -84,8 +84,17 @@ def __init__(self, rund, workflow, db_path=None):
                 self.db_point_fmt = self._get_db_point_format_compat()
                 self.c7_back_compat_mode = True
             except sqlite3.OperationalError:
+                with suppress(Exception):
+                    self.conn.close()
                 raise exc  # original error
 
+    def __enter__(self):
+        return self
+
+    def __exit__(self, exc_type, exc_value, traceback):
+        """Close DB connection when leaving context manager."""
+        self.conn.close()
+
     def adjust_point_to_db(self, cycle, offset):
         """Adjust a cycle point (with offset) to the DB point format.
 

tests/integration/test_dbstatecheck.py

@@ -52,13 +52,14 @@ async def checker(
     schd: Scheduler = mod_scheduler(wid, paused_start=False)
     async with mod_run(schd):
         await mod_complete(schd)
-        schd.pool.force_trigger_tasks(['1000/good'], [2])
+        schd.pool.force_trigger_tasks(['1000/good'], ['2'])
         # Allow a cycle of the main loop to pass so that flow 2 can be
         # added to db
         await sleep(1)
-        yield CylcWorkflowDBChecker(
+        with CylcWorkflowDBChecker(
             'somestring', 'utterbunkum', schd.workflow_db_mgr.pub_path
-        )
+        ) as _checker:
+            yield _checker
 
 
 def test_basic(checker):

tests/unit/test_db_compat.py

@@ -129,14 +129,13 @@ def test_cylc_7_db_wflow_params_table(_setup_db):
         rf'("cycle_point_format", "{ptformat}")'
     )
     db_file_name = _setup_db([create, insert])
-    checker = CylcWorkflowDBChecker('foo', 'bar', db_path=db_file_name)
+    with CylcWorkflowDBChecker('foo', 'bar', db_path=db_file_name) as checker:
+        with pytest.raises(
+            sqlite3.OperationalError, match="no such table: workflow_params"
+        ):
+            checker._get_db_point_format()
 
-    with pytest.raises(
-        sqlite3.OperationalError, match="no such table: workflow_params"
-    ):
-        checker._get_db_point_format()
-
-    assert checker.db_point_fmt == ptformat
+        assert checker.db_point_fmt == ptformat
 
 
 def test_pre_830_task_action_timers(_setup_db):