Set ['#default_value'] of taxonomy term reference field via hook_form_alter()?

Here's a different question with the same taxonomy term reference field I mentioned in my previous question.

Users with Administrator and Coach roles are granted permission to register Student users via a custom "Add student" form mode (user_add_student_form). It would be better for UX if I could set the ['#default_value'] of the select_a_school taxonomy term reference field to the same school that the currently logged in user belongs to.

I'm working with hook_form_alter() in template preprocess because that's how the previous developer set it up:

/**
 * Implements hook_form_alter().
 */
function projectname_form_alter(&$form, &$form_state, $form_id) {
  // Get the current User.
  $current_user_proxy = \Drupal::currentUser();
  $current_user_id = $current_user_proxy->id();
  if (!$current_user_proxy->isAnonymous()) {
    $currentUser = User::load($current_user_id);
    // Get the current User's school.
    $currentSchool = $currentUser->field_select_a_school->getValue();
    // Handle Add Student form.
    if ($form_id == 'user_add_student_form') {
      // This works.
      $form['account']['roles']['#access'] = FALSE;
      $form['account']['roles']['#default_value'] = [
        0 => 'authenticated',
        1 => 'student',
      ];
      // This does not work.
      $form['field_select_a_school']['#default_value'] = $currentSchool;
    }

Setting $form['account']['roles']['#default_value'] works as expected, but the taxonomy term reference field resists all such attempts.

I've tried the following variations:

      $form['field_select_a_school']['#default_value'] = $currentSchool;
      $form['field_select_a_school']['#default_value'][] = $currentSchool;
      $form['field_select_a_school']['widget']['#default_value'] = $currentSchool;
      $form['field_select_a_school']['widget']['#default_value'][] = $currentSchool;
      dump($currentSchool);

The Symfony VarDumper dump() of $currentSchool looks like it contains the correct data structure:

^ array:1 [▼
  0 => array:1 [▼
    "target_id" => "916"
  ]
]

Here, for reference, is the corresponding dump() for the target field in $form:

  "field_select_a_school" => array:8 [▼
    "#type" => "container"
    "#parents" => array:1 [▶]
    "#attributes" => array:1 [▶]
    "widget" => array:22 [▼
      "#title" => "Select A School*"
      "#description" => ""
      "#field_parents" => []
      "#required" => true
      "#delta" => 0
      "#weight" => 0
      "#element_validate" => array:1 [▶]
      "#key_column" => "target_id"
      "#type" => "select"
      "#options" => array:47 [▶]
      "#default_value" => []
      "#multiple" => false
      "#shs" => array:7 [▶]
      "#attributes" => array:1 [▶]
      "#attached" => array:1 [▶]
      "#entity_type" => "user"
      "#bundle" => "user"
      "#after_build" => array:1 [▶]
      "#field_name" => "field_select_a_school"
      "#parents" => array:1 [▶]
      "#tree" => true
      "#form_id" => "user_add_student_form"
    ]
    "#access" => true
    "#weight" => 22
    "#cache" => array:3 [▶]
    "#form_id" => "user_add_student_form"
  ]

No matter what I try, $form['field_select_a_school']['widget']['#default_value'] always ends up containing an empty array. ¯\_(ツ)_/¯

What am I missing here?