[Test] Add playwright test on connect to dom widget (#2912)

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browser_tests/assets/primitive_node_unconnected_dom_widget.json

@@ -0,0 +1,59 @@
+{
+  "last_node_id": 3,
+  "last_link_id": 1,
+  "nodes": [
+    {
+      "id": 1,
+      "type": "PrimitiveNode",
+      "pos": [14, 43],
+      "size": [203.1999969482422, 40.36840057373047],
+      "flags": {},
+      "order": 0,
+      "mode": 0,
+      "inputs": [],
+      "outputs": [
+        {
+          "name": "connect to widget input",
+          "type": "*",
+          "links": [],
+          "slot_index": 0
+        }
+      ],
+      "properties": {
+        "Run widget replace on values": false
+      }
+    },
+    {
+      "id": 2,
+      "type": "CLIPTextEncode",
+      "pos": [306.2463684082031, 45.30042266845703],
+      "size": [400, 200],
+      "flags": {},
+      "order": 1,
+      "mode": 0,
+      "inputs": [
+        {
+          "name": "clip",
+          "type": "CLIP",
+          "link": null
+        }
+      ],
+      "outputs": [
+        {
+          "name": "CONDITIONING",
+          "type": "CONDITIONING",
+          "links": null
+        }
+      ],
+      "properties": {
+        "Node name for S&R": "CLIPTextEncode"
+      },
+      "widgets_values": [""]
+    }
+  ],
+  "links": [],
+  "groups": [],
+  "config": {},
+  "extra": {},
+  "version": 0.4
+}