When opening the food menus tab on a site that already has some existing menu items, an empty loading state is displayed instead of the list of items.

To see the list of all existing menu items.
The site I tested on has a number of menu items previously added through wp-admin interface, but none showed on the list either.
I came across this issue, and I found some differences between WordPress.com Simple and Atomic sites:
I can still publish a Food menu item in Calypso from a WordPress.com Simple site, even though it won't show the published items in the dashboard.
However, I'm unable to publish anything in this module on an Atomic site. Instead, I receive this error message:
Publishing of Post Failed
I had another user report this issue in #680482-hc. It's a wpcom simple site on the business plan using the Aperitive theme. We could access the Food Menu CPT in WP Admin, but not in Calypso. I was able to confirm this on a test site, too.
Another report here:
https://en.forums.wordpress.com/topic/food-menus-not-showing-up
Another report today on a Simple site using the theme was APPETITE. It's a WordPress.com Simple site. The behavior was the same as Gracie described for simple sites above. 1273636-hc
User came to chat today with this issue as well. Appetite menus show up in WP-Admin, but their Calypso menu section is empty. Business Plan - Not AT.
Domain: thnbarandgrill.com
SA: https://wordpress.com/wp-admin/network/wpcom-paid-upgrades.php?action=search&username=thnbarandgrill
Username: thnbarandgrill
Also reported in #1533695-hc on a wpcom Simple site
Domain: https://ateliervermeer.ca/
Username: ateliervermeer
Theme: Aperitive
Another report on a Simple site using Restaurant: 1885148-hc
royalindiabelgium.com
I was able to reproduce on a test site.
Food Menus are shown as published, but are not accessible from Calypso. They can only be viewed and edited from WP Admin. https://cloudup.com/cNuTXRmOGwz
Also reported in #1692803-hc
Follow up in #1007086-zen
Site (simple site, Aperitive theme): https://courtclubitalia.com/
Also reported in #1121201-zen
Possibly related to https://github.com/Automattic/wp-calypso/issues/14442
Report in #3525705-hc with the Restaurant theme. In this one user has 30 menu items, but only 10 display in Calypso. I was able to recreate this on a test site. I initially had 14 items and everything was OK, but somewhere between 15 and 30 the behavior started. It looks like it displays all the items briefly, then hides everything but the first 10.
Another report, moved from https://github.com/Automattic/themes/issues/126
User report: #1822654-hc
Follow-up ticket: #1148472-zen
User's site: http://thefodband.wordpress.com
issue reported in #1227313-hc as well, nothing appears on Calypso for Food Menus but they have quite a bit set up (on the Premium plan)
Another user (christonite) reported they can't see the food menu they created with canape theme here: #5442926-hc
Site: foodbyami.wordpress.com
Another user (trattoria4mori) reported not seeing Food menu on Canape theme. Seemed to work using wp-admin.
Site: http://trattoria4mori.de
Another user in chat reported in not seeing posts she created in the Food Menu using the "Aperitive" theme. The posts show up on the frontend, but are missing from the Food Menus tab.
Plan: Premium
Theme: Aperitive
Site: chezmorasse.ca
Follow up ticket: 1530460-zen

However, when I attempted to replicate on my AT site (Activate Aperitive, Add new item under Food Menu, go back to Food Menus) I was able to see my post:

Another report on 1741817-Zen using the Canape (Canapé) theme.
Another report: 1808810-zen - Canape theme.
This came up in #10930868-hc on the Restaurant theme:
Is #3 related or would it be best to open up a separate issue for that?
Came across this in 1903280-zen with Aperitive.
User has several food-menu items added, but none is showing in Calypso. They are present in WP Admin.
This could be a good candidate for Calypsoify where the link is present in Calypso UI but when clicked loads the WP Admin view with Calypso CSS applied to it.
Changed from Bug to Enhancement since the content is accessible but it'd be even better to improve the flow so customers can edit and view all the CPTs as expected.
Got a user with the same situation on #2879730-hc. When troubleshooting I replicated the same situation Donal explains above.
Another case in #4373898-hc. The fact that Calypso says No Menu Items found even though the items are present, makes it seem like a bug to me. It's confusing for users who don't know to check WP Admin. It would be great to get this fixed.
Came across this in 1903280-zen with Aperitive.
User has several food-menu items added, but none is showing in Calypso. They are present in WP Admin.
Similar case here:
2042243-zen
Also with Aperitive.
Theme: Canape
This is a bug in the Jetpack/WP.com REST endpoints that list posts or fetch post counts for a particular CPT (nova_menu_item in case of Canape). That CPT is defined in the theme and the endpoint callback needs to do a call to
$this->load_theme_functions();
to define the CPT. Some endpoints do it, some don't.
Fixing in D31026-code.
@donpark Could you please take a look at the Phabricator patch from Jarda?
Reviewed and accepted @jsnajdr's patch with which Food Menus side menu now display food menu items.

Sidenote: This is unrelated to the patch nor this issue but I'm seeing X-Frame-Options related page crash when browser redirects to https://wordpress.com/block-editor/edit/nova_menu_item/{site_slug}/{post_id} after creating or updating a Food menu item.
Refreshing the crashed page loads the wp-admin Edit Menu Item page.
Pressing Update on the page again crashes the page.

UPDATE: Appears to be another X-Frame-Options related Block Editor issue, this time involving Calypsoify and wp-admin, which will take some to investigate unless there is someone who is up to speed on this stuff. Behavior is similar except, when redirecting, the page crashes immediately and, when reloading, the page takes a few seconds with some spinning feedback before it finishes loading.
D31026-code was deployed a moment ago. Jetpack PR to sync the changes to Jetpack/Atomic is open (not yet merged).
Most helpful comment
D31026-code was deployed a moment ago. Jetpack PR to sync the changes to Jetpack/Atomic is open (not yet merged).