Let document.hasStorageAccess check whether the Document already has unpartitioned data access

storage-access.bs

@@ -162,7 +162,15 @@ When invoked on {{Document}} |doc|, the <dfn export method for=Document><code>ha
 
     ISSUE: "same authority" here is a placeholder for a future concept that allows user agents to perform [=same site=] checks while adhering to additional security aspects such as the presence of a cross-site parent document, see [whatwg/storage#142](https://github.com/whatwg/storage/issues/142#issuecomment-1122147159). In practice, this might involve comparing the [=site for cookies=] or performing a [=same site=] check with the top-level document.
 
-1. [=Queue a global task=] on the [=permissions task source=] given |global| to [=/resolve=] |p| with |global|'s [=environment/has storage access=].
+1. Run the following steps [=in parallel=]:
+    1. Let <dfn>whether the user agent allows unpartitioned cookie access</dfn> be an algorithm that, given a user agent's settings object |user agent settings| and a [=boolean=] |has per-frame storage access|, runs the following steps:
+        1. [=Queue a global task=] on the [=permission task source=] given |global| to:
+            1. If |has per-frame storage access| is false:
+                1. If |user agent settings| allows unpartitioned cookie access, [=/resolve=] |p| with true and return |p|.
+            1. If |user agent settings| disallows unpartitioned cookie access, [=/resolve=] |p| with false and return |p|.
+            1. [=/Resolve=] |p| with true and return |p|.
+    1. Let |user agent settings| be user agent's settings.
+    1. Run <a href="#whether-the-user-agent-allows-unpartitioned-cookie-access">whether the user agent allows unpartitioned cookie access</a> with |user agent settings| and |global|'s [=environment/has storage access=].
 1. Return |p|.
 
 When invoked on {{Document}} |doc|, the <dfn export method for=Document><code>requestStorageAccess()</code></dfn> method must run these steps: