Changes to the alt text of images in the Media Library do not appear in posts

I have already created several posts with pictures. Some images are used in various posts. I have not entered an alt text for any image.

Today, I have added alt texts to many of my images in the Media Library. Unfortunately, I noticed that my newly added alt texts in the Media Library do not appear for any image in existing posts within the Gutenberg Editor.

Why is that and how can it be changed?