Edited block does not save: TypeError: Cannot read properties of null (reading 'classList')

Hmm... If I look at entity-form.js:217 I see that it's calling pageElementWrapper.classList.add('disabled-updating');. So, without editing if I just look at the markup of the page I should see markup that looks like this.

<div data-edit-plus-field-value-wrapper="node::2::field_summary::value" class="clearfix text-formatted field field--name-field-summary field--type-text-long field--label-hidden field__item">
  <div class="edit-plus-field-value" data-edit-plus-id="node::2::field_summary::0::en::full::text_long::text_default::value" data-edit-plus-page-element-id="node::2::field_summary::0::value" data-once="EditPlusDisabled">
    <p>Scrumptious vegan chocolate brownies that are rich, fudgy, and nutty. These delights have a surprise hint of coconut making them the perfect indulgence. Serve warm with a little vanilla dairy-free ice cream!</p>
  </div>
</div>

That markup is important as it allows the editor to relate the elements in the rendered page to the form items in the hidden entity form in the sidebar. The error is looking for data-edit-plus-field-value-wrapper in your markup which is added in edit_plus_preprocess_field. Are you overriding that field template? If so, could you pass along the attributes so the markup is more like what core ships with?

I added a dpm() inside edit_plus.module first to make sure that it reached that code and added the whole edit_plus_wrapper.
Screenshot 1 is dpm output for the textfield element I'm trying to change. it confirms that it does indeed reach that code and adds the edit_plus_wrapper.
The rest of the screenshots is to show that trhoughout the whole process, data-edit-plus-field-value-wrapper attribute is in fact present.

EditableElement.getPageElementWrapper() returns null, not sure yet why.
I added some output.

In comparison, the actual value of data-edit-plus-field-value-wrapper is:
block_content::54e7d573-bf17-40b1-bcad-2cca8ffb85bb::label::block_property
The ID that getPageElementWrapper() in editable-element.js is looking for is:
block_content::54e7d573-bf17-40b1-bcad-2cca8ffb85bb::text_body::value

So now its up to check why these two dont match.

You were spot on from the beginning: Our custom theme did have a field.html.twig override.
I removed that and all is working, so it was indeed caused by our custom theme.