The new feature is a consequence of SE responsive design efforts. See Editor improvements for images and links from Meta Stack Exchange:
Adding a link and image in your post is no longer done via pop up dialog. Instead the controls show up inline with the editor. This is sleeker and prepares the way for us to make our desktop theme work across all devices ...
It's still possible, but hidden.
@JoeFriend's answer to Can't upload image from URL anymore:
We no longer have an explicit entry point for this, but you can paste an image link when the uploader UX is showing.
Though at current writing, it might be still buggy for Edge browser.
If an answer is truly link only, I leave a comment explaining how that's frowned on and it's best to at least summarize the content, then I flag it. All but one time the answer has been converted to a comment (why it was disputed that one time, I have no idea).
If an answer contains links to supporting documentation that's another case, as with most of the ...
I think what you are referring to is the Linked section at right of any sites (like Stack Overflow) using the new CSS. Here that section is titled Related because we have not yet been upgraded to the new look.
What you are observing is the expected behaviour:
When your question is hosted on Stack Overflow what you will see under Linked are Stack Overflow ...
This was asked long ago but has not been answered.
To implement this would need to be a SE network-wide enhancement and much broader than the slight site customization that we can achieve internal to GIS SE.
Consequently, I recommend that you research it at Meta Stack Exchange instead of here. I just did and found the Q&A to Add explicit support for ...