Update image alt attribute globally (ie even if image is already in a post)

Hi! I added an alt tag to an image from the media library, however when I went to a previously published post that already had that image in it, I notice my alt tag is not there.

Is there a way to update my image alt in such a way that the all occurrences of it will also be updated (ie when they are used in a page/post)?

Also, if I add the alt tag in the media library and then add it to a post, will it be present there or will it be blank (haven’t tested this yet…)?

Thanks much!