How can I disable revisioning on specific node field

I currently use hook_entity_extra_field_info() and hook_ENTITY_TYPE_view() to create a custom field displayed in nodes that generates content dynamically via PHP.

However, Drupal 9 seems to be tracking changes to the output of this field each time I save a node revision, which I don't want because that field's content is generated dynamically and is already under version control in a custom module.

Is there a way to tell Drupal in one of those hooks, or anywhere else in the configuration, not to track revisions for a specific node field?

As the content of your field is dynamically generated, it sounds like you need a computed field. Which will remove the issue you are running into. A computed field is one that is generated dynamically, rather than through user input. As it is a field, it can be managed like any other field in Drupal (though integration with Views requires some additional efforts). Fields are also cached with Drupal's various cache APIs.

To create a computed field, first extend Drupal\Core\Field\FieldItemList, use the Drupal\Core\TypedData\ComputedItemListTrait, and implement the computeValue() method:

namespace Drupal\[EXAMPLE]\Plugin\Field;

use Drupal\Core\Field\FieldItemList;
use Drupal\Core\TypedData\ComputedItemListTrait;

class SomeDynamicField extends FieldItemList {

  use ComputedItemListTrait;      

  /**
   * {@inheritdoc}
   */
  protected function computeValue() {
    $values = some_function_to_get_an_array_of_values();
    foreach ($values as $index => $value) {
      $this->list[$delta] = $this->createItem($delta, $value);
    }
  }
}

Next, this field needs to be added to each entity type that you need, in hook_entity_base_field_info_alter():

use Drupal\Core\Entity\EntityTypeInterface;
use Drupal\Core\Field\BaseFieldDefinition;

/**
 * Implements hook_entity_base_field_info_alter().
 */
function EXAMPLE_entity_base_field_info_alter(&$fields, EntityTypeInterface $entity_type) {
  // Add/alter entity types as necessary.
  $applicable_entity_types = ['node'];
  if (in_array($entity_type->id(), $applicable_entity_types)) {
    $fields['my_computed_field'] = BaseFieldDefinition::create('string')
      ->setName('example_field')
      ->setLabel(t('Example Calculated Field'))
      ->setDescription(t('An example of a calculated field'))
      // Set the field as a computed field.
      ->setComputed(TRUE)
      // Set the class that generates the field value(s).
      ->setClass('\Drupal\[EXAMPLE]\Plugin\Field\Computed\SomeDynamicField');
  }
}