Make postmaster 003_start_stop.pl test less flaky

The test is very sensitive to how backends start and exit, because it
tests dead-end backends which occur when all the connection slots are
in use. The test failed occasionally in the CI, when the backend that
was launched for the raw_connect_works() check lingered for a while,
and exited only later during the test. When it exited, it released a
connection slot, when the test expected all the slots to be in use at
that time.

The 002_connection_limits.pl test had a similar issue: if the backend
launched for safe_psql() in the test initialization lingers around, it
uses up a connection slot during the test, messing up the test's
connection counting. I haven't seen that in the CI, but when I added a
"sleep(1);" to proc_exit(), the test failed.

To make the tests more robust, restart the server to ensure that the
lingering backends doesn't interfere with the later test steps.

In the passing, fix a bogus test name.

Report and analysis by Jelte Fennema-Nio, Andres Freund, Thomas Munro.

Discussion: https://www.postgresql.org/message-id/CAGECzQSU2iGuocuP+fmu89hmBmR3tb-TNyYKjCcL2M_zTCkAFw@mail.gmail.com
Backpatch-through: 18

src/test/postmaster/t/002_connection_limits.pl

@@ -74,6 +74,11 @@ sub connect_fails_wait
 	ok(1, "$test_name: client backend process exited");
 }
 
+# Restart the server to ensure that any backends launched for the
+# initialization steps are gone. Otherwise they could still be using
+# up connection slots and mess with our expectations.
+$node->restart;
+
 my @sessions = ();
 my @raw_connections = ();
 

src/test/postmaster/t/003_start_stop.pl

@@ -46,6 +46,11 @@ if (!$node->raw_connect_works())
 	plan skip_all => "this test requires working raw_connect()";
 }
 
+# Restart the server to ensure that the backend launched for
+# raw_connect_works() is gone. Otherwise, it might free up the
+# connection slot later, when we expect all the slots to be in use.
+$node->restart;
+
 my @raw_connections = ();
 
 # Open a lot of TCP (or Unix domain socket) connections to use up all
@@ -81,7 +86,7 @@ for (my $i = 0; $i <= 20; $i++)
 # clients already" instead of "role does not exist" error. Test that
 # to ensure that we have used up all the slots.
 $node->connect_fails("dbname=postgres user=invalid_user",
-	"connect ",
+	"connection is rejected when all slots are in use",
 	expected_stderr => qr/FATAL:  sorry, too many clients already/);
 
 # Open one more connection, to really ensure that we have at least one