In block themes you can have blocks live inside the template but still have part of their content editable. So for example the post title & post featured image blocks allow you to still edit their content when the "Show Template" option is active.

This functionality only works if the fields that are editable save to something other than local block attributes.

Currently the Custom CSS field which was added in #73959 that lives inside the advanced inspector is still visible and editable in that preview. But the value cannot get saved.

The solution here should be that the field is hidden in that mode same as all of the other fields.