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
5. https://mathoverflow.net/questions/30136
6. [Topological scaling (?)](https://mathoverflow.net/a/35780)
7. <s>https://mathoverflow.net/questions/375339</s>
    
    This gif has been replaced and it seems to be the correct one.
    
8. https://mathoverflow.net/questions/38236
9. https://mathoverflow.net/questions/39637
10. https://mathoverflow.net/questions/56138
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.)