Updates Playwright to 1.37.1 from 1.33 (#39815)

Co-authored-by: Jon Lane <jon.lane@automattic.com>

plugins/woocommerce/changelog/e2e-update-playwright-to-1_37_1

@@ -0,0 +1,4 @@
+Significance: patch
+Type: dev
+
+Updates Playwright from 1.33 to 1.37.1

plugins/woocommerce/package.json

@@ -58,7 +58,6 @@
 		"@babel/core": "7.12.9",
 		"@babel/preset-env": "7.12.7",
 		"@babel/register": "7.12.1",
-		"@playwright/test": "^1.33.0",
 		"@typescript-eslint/eslint-plugin": "^5.54.0",
 		"@typescript-eslint/experimental-utils": "^5.54.0",
 		"@typescript-eslint/parser": "^5.54.0",
@@ -117,6 +116,7 @@
 		"ie 9"
 	],
 	"dependencies": {
+		"@playwright/test": "^1.37.1",
 		"@wordpress/browserslist-config": "wp-6.0"
 	}
 }