Problem/Motivation
When Layout Builder and Quick Edit are enabled, it's expected that Entity Fields are still quick-editable when rendered by the Field Block. It appears that the expected data-quickedit-field-id attributes are not being output, and as a result no fields are quick-editable when Layout Builder is enabled.
Proposed resolution
Panelizer has this exact same problem, which was addressed in #2693163: Quick Edit support for fields displayed using the ctools_field block.. We can probably replicate the logic and tests there in Layout Builder without any issues.
Remaining tasks
Write and review a patch.
User interface changes
None.
API changes
\Drupal\layout_builder\Entity\LayoutEntityDisplayInterface::getRuntimeSections() is now a public method.
Data model changes
None.