Use lock to limit concurrent connection opening in pool.

lib/src/pool/pool_impl.dart

@@ -2,10 +2,10 @@ import 'dart:async';
 
 import 'package:collection/collection.dart';
 import 'package:pool/pool.dart' as pool;
-import 'package:postgres/src/v3/resolved_settings.dart';
 
 import '../../postgres.dart';
 import '../v3/connection.dart';
+import '../v3/resolved_settings.dart';
 
 EndpointSelector roundRobinSelector(List<Endpoint> endpoints) {
   int nextIndex = 0;
@@ -26,6 +26,10 @@ class PoolImplementation<L> implements Pool<L> {
     _maxConnectionCount,
     timeout: _settings.connectTimeout,
   );
+  late final _connectLock = pool.Pool(
+    1,
+    timeout: _settings.connectTimeout,
+  );
 
   PoolImplementation(this._selector, PoolSettings? settings)
       : _settings = ResolvedPoolSettings(settings);
@@ -173,32 +177,34 @@ class PoolImplementation<L> implements Pool<L> {
       return oldc;
     }
 
-    while (_connections.length == _maxConnectionCount) {
-      final candidates =
-          _connections.where((c) => c._isInUse == false).toList();
-      if (candidates.isEmpty) {
-        throw StateError('The pool should not be in this state.');
+    return await _connectLock.withResource(() async {
+      while (_connections.length >= _maxConnectionCount) {
+        final candidates =
+            _connections.where((c) => c._isInUse == false).toList();
+        if (candidates.isEmpty) {
+          throw StateError('The pool should not be in this state.');
+        }
+        final selected = candidates.reduce(
+            (a, b) => a._lastReturned.isBefore(b._lastReturned) ? a : b);
+        await selected._dispose();
       }
-      final selected = candidates
-          .reduce((a, b) => a._lastReturned.isBefore(b._lastReturned) ? a : b);
-      await selected._dispose();
-    }
 
-    final newc = _PoolConnection(
-      this,
-      endpoint,
-      settings,
-      await PgConnectionImplementation.connect(
+      final newc = _PoolConnection(
+        this,
         endpoint,
-        connectionSettings: settings,
-      ),
-    );
-    newc._isInUse = true;
-    // NOTE: It is important to update _connections list after the isInUse
-    //       flag is set, otherwise race conditions may create conflicts or
-    //       pool close may miss the connection.
-    _connections.add(newc);
-    return newc;
+        settings,
+        await PgConnectionImplementation.connect(
+          endpoint,
+          connectionSettings: settings,
+        ),
+      );
+      newc._isInUse = true;
+      // NOTE: It is important to update _connections list after the isInUse
+      //       flag is set, otherwise race conditions may create conflicts or
+      //       pool close may miss the connection.
+      _connections.add(newc);
+      return newc;
+    });
   }
 }