I encountered this issue when upgrading from Drupal 8 to  

Mismatched entity and/or field definitions The following changes were detected in the entity type and field definitions. Paragraph The paragraph.field_background_fixed field needs to be updated.

Since <drush entup> is deprecated you would need to install the Devel Entity Updates for this. How I fixed this was to write a simple hook_update() function in my custom module:

 * Drupal 9 upgrade: "Mismatched entity and/or field definition” when “drush entity-updates” fails?"
function mymodule_update_9020() {
  $manager = \Drupal::entityDefinitionUpdateManager();
  if ($field = $manager->getFieldStorageDefinition('field_background_fixed', 'paragraph')) {

After the update, the error disappeared!

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