Suggested storage access API improvements

### MDN URL

https://developer.mozilla.org/en-US/docs/Web/API/Storage_Access_API

### What specific section or headline is this issue about?

_No response_

### What information was incorrect, unhelpful, or incomplete?

In https://github.com/mdn/content/pull/42432, we updated the Storage Access API docs to indicate that, when embedded content activates a previously-granted storage-access permission via the `requestStorageAccess()` method or the `Activate-Storage-Access` header, 3rd party cookies are now only sent with requests to the calling embed's exact origin.

In doing this, we uncovered a few other improvements that could stand to be made to these docs:

1. In general, we should check the docs to make sure they are inverted to "use the headers unless you need to use the API". This has bene done in some places, but the API landing page overview needs some work, and possibly other places too.
2. The https://developer.mozilla.org/en-US/docs/Web/API/Storage_Access_API/Using guide is out of date and needs some updates.
3. Check this thread to see if anything else needs doing according to it: https://github.com/mdn/content/pull/42432#pullrequestreview-3585074137

### What did you expect to see?

See above

### Do you have any supporting links, references, or citations?

_No response_

### Do you have anything more you want to share?

_No response_