Undefined property notice when editing Custom Styles on book in staging environment

Prerequisites

[x] Can you reproduce the behavior you wish to address with all other plugins deactivated?
[x] Are you running the latest version of Pressbooks and the latest version of WordPress?
[x] Are you experiencing this issue with one of our built-in root or book themes?
[x] Did you perform a cursory search to see if your bug or enhancement is already listed?

Description

When I attempt to save the custom CSS for the Open Textbooks with Students book on integrations (https://integrations.pressbooks.network/opentextbookswithstudents/wp-admin/themes.php?page=pb_custom_styles&slug=web), I see a Notice: Undefined property: stdClass::$edit_page in /srv/www/integrations.pressbooks.network/releases/20210227030651/web/wp/wp-includes/capabilities.php on line 166 message. The notice appears to be related to the way that custom post types are registered with WordPress (perhaps this issue is related to https://github.com/pressbooks/pressbooks/issues/2079?): https://github.com/WordPress/WordPress/blob/071a41414a86a528db349d8bd257a72b21b19e8d/wp-includes/capabilities.php#L157-L172

The CSS changes do appear to be saved and are functional in the book following the clearing of the notice. I have not observed the notice in other books on this or other networks (tested in sample books on integrations, textopress, and university networks). The notice is displayed when edits are made to the webbook, ebook, and PDF custom styles for this particular book.

Steps to Reproduce

Visit https://integrations.pressbooks.network/opentextbookswithstudents/wp-admin/themes.php?page=pb_custom_styles&slug=web
Enter or change the custom CSS in any of the stylesheets
Observe a brief notice appear on the screen

This video shows the expected behavior seen in one book on the integrations network, followed by the unexpected behavior seen in the Open Textbooks with Students text: https://user-images.githubusercontent.com/13485451/109693514-99980e00-7b3e-11eb-9317-0a5c2ec13fd0.mp4

Expected behavior: CSS changes are saved with no notice.

Actual behavior: An unexpected notice is displayed before the CSS changes are saved.

Notes: the notice can be reproduced in some but not all books on the integrations network. For example, the notice does appear on https://integrations.pressbooks.network/h5p-clone/wp-admin/themes.php?page=pb_custom_styles but does not appear on https://integrations.pressbooks.network/newbook/wp-admin/themes.php?page=pb_custom_styles&slug=web or https://integrations.pressbooks.network/epubimport/wp-admin/themes.php?page=pb_custom_styles&slug=web. I cannot yet determine why the notice only appears on some books and not others.

See https://sentry.io/organizations/pressbooks/issues/2247121159/?environment=staging&project=3954026&query=edit_page&statsPeriod=14d for the issue in Sentry

pressbooks / pressbooks