Problems with Quick Edit and Media embed

Problem/Motivation

Using Quick Edit, it is not possible to insert a media element with CKEditor 5.

Using the Umami theme, the console shows:
Uncaught Error: Quick Edit could not associate the rendered entity field markup (with [data-quickedit-field-id="..."]) with the corresponding rendered entity markup: no parent DOM node found with [data-quickedit-entity-id="..."]. This is typically caused by the theme's template for this entity type forgetting to print the attributes.

This may be an Umami problem, and not a CKEditor 5 problem, however the drupalMedia plugin is also not loading correctly.
Console also shows:

toolbarview-item-unavailable 
Object { name: "drupalMedia" }

Steps to reproduce

Edit a node, insert a media element using CKEditor 5.
Visit the node, enable quickedit.
Media embed toolbar item is missing and console shows 1 or both warnings.

Proposed resolution