"I've already described the image in the post! Do I still need an alt-text?"

Yes, you do.

In fact, unless your image description exceeds 1,500 characters or contains any information that can neither be found in the image itself nor in the post text outside the image description, it belongs only into the alt-text.

And if it is longer than 1,500 characters, and/or it contains extra information, there should be a purely visual description with no extra information in the alt-text in addition to the full description in the post.

This doesn't have as much to do with accessibility as it does with Fediverse or rather Mastodon culture: The lack of sufficient alt-text is reason enough for many to sanction you, often in ways that really cost you reach in the Fediverse.