There are two types of posts on SN, ... Link posts and Discussion posts. On a Discussion post, there's no automatic rendering if you include the URL for a Tweet.

For link posts, SN has added a Twitter embed feature.

Thus when you view an SN item that is a Link post using the URL for a Tweet, it will have an embed area near the top where there is Twitter embed code that renders the Tweet nearly identically to how it looks in Twitter. But because heights of a Tweet can vary, that embed can get cut off at a certain height, and to see the full Tweet you need to click Show Full Tweet.

This works for posts that are for a Tweet with an image or images, with an audio, and with a video as well. Essentially, however it appears on Twitter.com is how it will look in the embed.

I can't say that I've seen a Twitter URL that didn't render in the embed. It's possible that could occur, I've just not seen it. Maybe your Twitter link was messed up somehow?

Now for meme images and such, a Twitter embed that gets cut off halfway (until you click "Show full Tweet" kind of sucks. A meme image hits best when seen in its entirety, and all at once -- no interaction.

On of the earliest feature requests in the Stacker News Github repo (Issue #9) is for additional post types, including Image and Video (uploads, I think). That requires storage for hosting / CDN and such, so I can see why that hasn't been added just yet, especially when there's a workaround: markdown supports images

Why is there no option to upload an image to these SN posts? #11538

So if you want an SN item to be an image, simply create a Discussion post and use the markdown for image and in that use the image's URL.