Not an answer, but doesn't really fit in a comment.

Glorfindel ran a script to find and try to repair/replace linked images. [His answer](https://meta.stackexchange.com/a/388726) includes a link to a (very long) output of results. Searching for "mathoverflow" jumps to the results for MathOverflow (and also meta.mathoverflow). Many images were successfully replaced. There are only a handful of uncertainties or failures. Here they are (I "snipped" out the successful replacements):

    ## mathoverflow.net

    ### Successful replacements

    [snip]

    ### Uncertainties

    | Frequency | URL | Replacement | Post IDs |
    |----------:|-----|-------------|----------|
    | 1 | https://i.imgur.com/KFkbXCz.gif | Not uploaded but archived as https://web.archive.org/web/20230503101817/https://i.imgur.com/KFkbXCz.gif | 291829 |
    | 1 | https://i.imgur.com/p7zUONx.gif | Not uploaded but archived as https://web.archive.org/web/20230503101846/https://i.imgur.com/p7zUONx.gif | 375339 |

    ### Failures

    | Frequency | URL | Failure | Post IDs |
    |----------:|-----|---------|----------|
    | 1 | https://i.imgur.com/76yeO.png | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Invalid Content-Type application/octet-stream returned for https://web.archive.org/web/20150427162752///i.imgur.com/76yeO.png | 39637 |
    | 1 | https://i.imgur.com/7ctju.gif | Not found in Wayback Machine. | 30136 |
    | 1 | https://i.imgur.com/Gnpdn.png | Not found in Wayback Machine. | 25897 |
    | 1 | https://i.imgur.com/RleJK.png | Not found in Wayback Machine. | 30136 |
    | 1 | https://i.imgur.com/bj5zs.png | Not found in Wayback Machine. | 30136 |
    | 1 | https://i.imgur.com/cZKaB.gif | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Broken image, an error image is served instead. | 24272 |
    | 1 | https://i.imgur.com/pChFw.png | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Broken image, an error image is served instead. | 56138 |
    | 1 | https://i.imgur.com/xAZZb.png | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Broken image, an error image is served instead. | 38236 |
    | 1 | https://imgur.com/F1x6j.png | ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Not found in Wayback Machine. | 35780 |
    | 1 | https://imgur.com/drlwRgv | DownloadFailedException: Image not found on imgur image page. | 168300 |
    | 1 | https://imgur.com/xjxWV.gif | ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Not found in Wayback Machine. | 24272 |

    ## meta.mathoverflow.net

    ### Successful replacements

    [snip]

    ### Failures

    | Frequency | URL | Failure | Post IDs |
    |----------:|-----|---------|----------|
    | 1 | https://i.imgur.com/76yeO.png | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Invalid Content-Type application/octet-stream returned for https://web.archive.org/web/20150427162752///i.imgur.com/76yeO.png | 5551 |
    | 1 | https://i.imgur.com/cZKaB.gif | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Broken image, an error image is served instead. | 5551 |
    | 1 | https://i.imgur.com/pChFw.png | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Broken image, an error image is served instead. | 5551 |
    | 1 | https://i.imgur.com/xAZZb.png | com.stackexchange.toolbox.editor.ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Broken image, an error image is served instead. | 5551 |
    | 1 | http://imgur.com/ | ProcessImageException: com.stackexchange.toolbox.editor.DownloadFailedException: Invalid Content-Type text/html returned for https://web.archive.org/web/20230509011314/https://imgur.com/ | 773 |

Here is my attempt to make easier links to the MO and meta.MO posts (some of them have several broken/missing images, I just put one link for each post):

1. https://mathoverflow.net/questions/168300
2. https://mathoverflow.net/questions/24272
3. https://mathoverflow.net/questions/25897
4. https://mathoverflow.net/questions/291829

    This gif is on `imgur.com`. It's too big to upload to `stack.imgur.com` (about 4.6MB). It seems to be in the [Wayback Machine](http://web.archive.org/web/20230513034720/https://imgur.com/KFkbXCz)
    
5. https://mathoverflow.net/questions/30136
6. [Topological scaling (?)](https://mathoverflow.net/a/35780)
    
    The answer included a reference to the paper that the (now lost) image was taken from. I copied the image again and uploaded it.
    
    (The image has two parts marked (a) and (b), and caption text. I'm not sure if the original included all of that, or maybe just the (b) image. I decided to include all of it.)
    
7. [Which subsets of the plane are similar to all their affine images?](https://mathoverflow.net/q/375339)
    
    This gif is on `imgur.com`. It's too big to upload to `stack.imgur.com`. It seems to be in the [Wayback Machine](https://web.archive.org/web/20210506161914/https://i.imgur.com/p7zUONx.gif)
    
8. https://mathoverflow.net/questions/38236
9. https://mathoverflow.net/questions/39637
10. https://mathoverflow.net/questions/56138

    Replaced image with tex (as suggested in chat)
    
11. https://meta.mathoverflow.net/questions/5551
12. [How to post a file](https://meta.mathoverflow.net/a/773) (This answer contains only a link to imgur.com, not to a specific picture.)