How to add/install a new field to all bundles of certain entity types?

I need to add a new string field called instagram_owner to all bundles of nodes, media and file entities. If new bundles are created, I need the field on them too. This is what I have so far in my MODULE_NAME.module file.

use Drupal\Core\Field\BaseFieldDefinition;
use Drupal\Core\StringTranslation\TranslatableMarkup;
use Drupal\Core\Entity\EntityTypeBundleInfo;
use Drupal\Core\Entity\EntityFieldManager;

/**
 * Implements hook_entity_base_field_info().
 */
function MODULE_NAME_entity_base_field_info(\Drupal\Core\Entity\EntityTypeInterface $entity_type) {
    $entity_type_id = $entity_type->id();
    $field_name = 'instagram_owner';
    
    // Check for the entity types
    if ($entity_type_id === 'node' || $entity_type_id === 'media' || $entity_type_id === 'file') { 
        
        // Specify new Instagram owner field
        $fields[$field_name] = BaseFieldDefinition::create('string')
            ->setLabel(new TranslatableMarkup("Instagram owner id"))
            ->setDescription(new TranslatableMarkup("This is the owners Instagram ID"))
            ->setSettings(["max_length" => 255, "text_processing" => 0])
            ->setDefaultValue("")
            ->setDisplayOptions("view", ["label" => "above", "type" => "string", "weight" => -3])
            ->setDisplayOptions("form", ["type" => "string_textfield", "weight" => -3]);
        
        // Get the bundles for this entity type
        $bundle_service = \Drupal::service('entity_type.bundle.info');
        $bundles = $bundle_service->getBundleInfo($entity_type_id);
        
        foreach($bundles as $bundle_id => $bundle) {
            
            // Check to see if our field already exists on this bundle
            $bundle_fields = \Drupal::service('entity_field.manager')->getFieldDefinitions($entity_type_id, $bundle_id);
            if (!isset($bundle_fields[$field_name])) {
                
                // If not, install it...
                // not sure if this will install the field either? 
                // Where do I get $storage_definition from? This has never been uncommented.
                // BaseFieldDefinition::installFieldStorageDefinition($field_name, $entity_type_id, $bundle_id, FieldStorageDefinitionInterface $storage_definition);
                
            }
        }
        return $fields;
    }
    
}

I know that the problematic line seems to be this one. It's this that throws a 503 error page:

$bundle_fields = \Drupal::service('entity_field.manager')->getFieldDefinitions($entity_type_id, $bundle_id);

In devels php block I get the expected results. I'm using this for testing:

    $entity_type_id = 'node';
    $field_name = 'instagram_owner';

    if ($entity_type_id === 'node' || $entity_type_id === 'media' || $entity_type_id === 'file') {        
                
        $bundle_service = \Drupal::service('entity_type.bundle.info');
        $bundles = $bundle_service->getBundleInfo($entity_type_id);
        dpm($bundles);
        $field_service = \Drupal::service('entity_field.manager');
        foreach($bundles as $bundle_id => $bundle) {
            $bundle_fields = $field_service->getFieldDefinitions($entity_type_id, $bundle_id);
            if (!isset($bundle_fields[$field_name])) {
                
                $ready_to_install = 'yes';
                dpm($ready_to_install);
                
            }
        }
        dpm($bundle_fields);
    }

Any help would be greatly appreciated.

There were a few pieces of the puzzle I hadn't understood. Firstly, hook_entity_base_field_info() just defines the specification of the base field. I originally thought I also had to install the field on each bundle within that hook. Not true.

Once the field was defined in this hook, the field appears on every bundle because it is a base field. However values won't actually get saved.

So the next thing I couldn't get my head around was how to install the schema to store the values. I learned that this can be taken care of with hook_install, hook_uninstall and if needed hook_update_N.

So, 3 days of pain later, this is what I ended up with:

my_module.module

/**
 * Implements hook_entity_base_field_info().
 */
function MY_MODULE_entity_base_field_info(\Drupal\Core\Entity\EntityTypeInterface $entity_type) {
    
    // Only install on nodes and media.
    $entity_type_id = $entity_type->id();
    if ($entity_type_id === 'node' || $entity_type_id === 'media') { 
        if ($entity_type_id === 'node') {
            $field_name = 'instagram_owner_display';
        }
        elseif ($entity_type_id === 'media') {
            $field_name = 'instagram_owner_media';
        }
        
        // Specify new Instagram owner field
        $fields[$field_name] = BaseFieldDefinition::create('string')
            ->setLabel(new TranslatableMarkup("Instagram owner ID"))
            ->setDescription(new TranslatableMarkup("This is the Instagram Account ID of who imported this."))
            ->setSettings(["max_length" => 255, "text_processing" => 0])
            ->setDefaultValue("")
            ->setDisplayOptions("view", ["label" => "above", "type" => "string"])
            ->setDisplayOptions("form", ["type" => "string_textfield"]);
        return $fields;
    }
}

my_module.install

/**
 * Implements hook_install().
 */
function MY_MODULE_install() {
    
    // Install Instagram owner field on nodes and media
    $field_manager = \Drupal::service('entity_field.manager'); 
    $field_storage_manager = \Drupal::service('field_storage_definition.listener'); 
    
    $node_definition = $field_manager->getFieldStorageDefinitions('node')['instagram_owner_display']; 
    $field_storage_manager->onFieldStorageDefinitionCreate($node_definition);
    
    $media_definition = $field_manager->getFieldStorageDefinitions('media')['instagram_owner_media'];
    $field_storage_manager->onFieldStorageDefinitionCreate($media_definition);
}

/**
 * Implements hook_uninstall().
 */
function MY_MODULE_uninstall() {
    
    // Delete Instagram owner field on nodes and media
    $field_manager = \Drupal::service('entity_field.manager'); 
    $field_storage_manager = \Drupal::service('field_storage_definition.listener'); 
    
    $node_definition = $field_manager->getFieldStorageDefinitions('node')['instagram_owner_display']; 
    $field_storage_manager->onFieldStorageDefinitionDelete($node_definition);
    
    $media_definition = $field_manager->getFieldStorageDefinitions('media')['instagram_owner_media'];
    $field_storage_manager->onFieldStorageDefinitionDelete($media_definition);
}

/**
 * Install the new Instagram owner field on existing media and node bundles.
 */
function MY_MODULE_update_N() {
    
    // Install Instagram owner field on nodes and media
    $field_manager = \Drupal::service('entity_field.manager'); 
    $field_storage_manager = \Drupal::service('field_storage_definition.listener'); 
    
    $node_definition = $field_manager->getFieldStorageDefinitions('node')['instagram_owner_display']; 
    $field_storage_manager->onFieldStorageDefinitionCreate($node_definition);
    
    $media_definition = $field_manager->getFieldStorageDefinitions('media')['instagram_owner_media'];
    $field_storage_manager->onFieldStorageDefinitionCreate($media_definition);
}