Thanks for your update with the additional information. I am able to reproduce your steps and match the results you posted in your screen shots.
The MLA Quick Edit area allows you to update the database information associated with a Media Library item. The fact that you can see the correct results in the Media/Assistant submenu table column and in the Media/Edit Media screen shows that this is working properly.
Your final screen shot, 5-23-30, shows the “Classic Editor” Visual tab. This confirms that the problem is not in the database but in the content WordPress adds to the post/page when you insert an image. If you change to the Text tab you will see something like this:
<img class="alignnone size-medium wp-image-8171" src="https://l.mladev/wp-content/uploads/2021/09/Screenshot-2020-08-03-at-17.13-1-300x232.jpg" alt="" width="300" height="232" />
When you insert the image, WordPress copies information such as the ALT Text from the database and hard-codes it into the IMG tag added to the post/page content. If you change the database information later, neither WordPress nor MLA will go searching through all your posts/pages looking for inserts that must also be updated. This is a very common issue/problem.
The current MLA version includes the “MLA Insert Fixit” example plugin that contains a number of tools for updating IMG tags in post/page inserts. You can find details in this earlier support topic:
Update ALT tags in posts from media library ALT tags
I hope the tools in the example plugin will help you achieve your goal. I am marking this topic resolved, but please update it if you have any problems or further questions regarding the solution provided by the example plugin.