I set an image/file attribute, with the setting option Input Format = HTML Input.
This HTML Input option displays image/file input form as shown below.

I put an image on the composer and publish a page, the file is not saved.
I put an image on the composer and save a page as draft, the file is saved.

Is the purpose of this to not use the file manager / file picker? I’m not sure how the HTML input format would work in this context of a page attribute.
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Is the purpose of this to not use the file manager / file picker?
That’s right. Because HTML input form is easy to use for those unfamiliar with computers.
I could be wrong but I think the main purpose of the HTML input is just to receive files, not to show them thereafter or maintain them.
It seems an issue with the HTML form. The file specified is not uploaded.
There must be something wrong when uploading or saving a file via the HTML form.