For the published post to use the included image as the front page thumbnail, as it does for posts published in the Classic Editor or Calypso, and for the featured image to be displayed on the single post view, depending on the theme.
The post is displayed on the front page as if there is no featured image set, and no featured images displays in the single post view either.

This appears to only happen in Core - I'm not able to replicate this on a WordPress.com site with Gutenberg enabled.
Issue found during general Gutenberg testing.
I dug into this issue a bit after chatting about it recently with @alaczek after she ran into it during some development work.
In testing, I found:
Jetpack_PostImages::from_html isn't returning anything on the Gutenberg side, so it's definitely related to the Jetpack_PostImages class, not Content Options itself.Next steps
@davidakennedy any progress on this yet?
I've noticed on the Photo Blog theme that images added in Gutenberg also won't trigger the fullbleed class that makes images and galleries display larger in the Modern style pack. I haven't reported it yet as I still wanted to do more testing to confirm, but might that be caused by the same issue?
That is because the markup of images inserted via a Gutenberg block is different from the markup used with the classic editor.
<!-- wp:image {"id":12375} -->
<figure class="wp-block-image"><img src="https://mysite.com/wp-content/uploads/2018/09/dora-reis-249014-unsplash.jpg" alt="" class="wp-image-12375"/></figure>
<!-- /wp:image -->
<img src="https://mysite.com/wp-content/uploads/2018/09/dora-reis-249014-unsplash.jpg" alt="" width="3008" height="2000" class="alignnone size-full wp-image-12375" />
The big difference here is that Gutenberg does not include any width or height tags. That is a problem here, because Jetpack relies on those tags to figure out if an image is large enough to be used elsewhere (in theme tools like Content Options, but also in Open Graph Meta Tags, Related Posts, Publicize, ...).
Since Jetpack does not know how big the image is, it ignores it.
This difference between the classic editor and Gutenberg was highlighted here:
https://github.com/WordPress/gutenberg/issues/6652
And a PR was created to add those tags back to Gutenberg:
https://github.com/WordPress/gutenberg/pull/9421
Once that PR is merged, I believe our problem should be solved.
I'll close this issue since it seems to be something that will be fixed in Gutenberg directly.
Noting that for now, one can bypass this issue by adding the following to a functionality plugin:
add_filter( 'jetpack_postimages_ignore_minimum_dimensions', '__return_true' );
It forces Jetpack to consider all images as good, even when it does not know their dimensions.
@KokkieH it's not the same issue as this ticket, although still related to Gutenberg image output. The script used in Photo Blog is looking for .size-full class being added to the image, and makes those images slightly larger. I moved it to a ticket, where we can discuss further: 2484-wpcom-premium-themes
Most helpful comment
That is because the markup of images inserted via a Gutenberg block is different from the markup used with the classic editor.
When using Gutenberg and an image block
Insert the same image using the classic editor:
The big difference here is that Gutenberg does not include any
widthorheighttags. That is a problem here, because Jetpack relies on those tags to figure out if an image is large enough to be used elsewhere (in theme tools like Content Options, but also in Open Graph Meta Tags, Related Posts, Publicize, ...).Since Jetpack does not know how big the image is, it ignores it.
This difference between the classic editor and Gutenberg was highlighted here:
https://github.com/WordPress/gutenberg/issues/6652
And a PR was created to add those tags back to Gutenberg:
https://github.com/WordPress/gutenberg/pull/9421
Once that PR is merged, I believe our problem should be solved.
I'll close this issue since it seems to be something that will be fixed in Gutenberg directly.