Custom field type properties populated by fetched data

I have a custom field type, org_person, with an autocomplete set up on it to search our endpoint of "people". It saves something like John Smith (12345) to the value property ($properties['value']).

The endpoint looks something like this:

[{id, name, title, ...}, {id, name, title, ...},...]

My goal is to, on entity save (and cron), query my endpoint and save the 30+ properties to the database.

I need to be able to filter and sort on these values in views which is why computing this data in real-time is off the table.

As I understand it, I need to set the class of the property to use for generating the property value. Something like:

    $properties['name'] = DataDefinition::create('any')
      ->setLabel(new TranslatableMarkup('Name'))
      ->setComputed(TRUE)
      ->setReadOnly(TRUE)
      ->setClass('\Drupal\my_module\TypedDataName');

Then in my TypedDataName Class, I get the value like:

  public function getValue() {
    if ($this->processed !== NULL) {
      return $this->processed;
    }

    $values = $this->getParent()->getValue();
    $submitted_value  = $values['value'];

    $id = EntityAutocomplete::extractEntityIdFromAutocompleteInput($submitted_value);

    // Runs fetch here to get 'name' property
    $response = $this->_fetchName($id);
    $value = $response[0]["name"];

    $this->processed = $value;

    return $this->processed;
  }

This works, although it seems like it's running on display instead of pulling from the database.

Also, if I added another property, like title (or the rest of them), it's going to run this fetch on every property.

How can this be done with a single fetch to populate the 30+ properties on save?