Drupal - How to rebuild form after AJAX call

First problem is to handle the value for the column number. On the first build get it from configuration, on a rebuild get it from the user input and put it in $columnNum.

The second is to decide, what part of the form changes in AJAX and put this in a div container with the id columns-wrapper.

class AJAXexample extends BlockBase {
    public function blockForm($form, FormStateInterface $form_state) {
        $columnNum = empty($form_state->getValue('columnNum')) ? $this->configuration['columnNum'] : $form_state->getValue('columnNum');
        $form['columnNum'] = [
            '#title'   => t('Number of Columns'),
            '#type'    => 'select',
            '#options' => [
                1         => '1',
                2         => '2',
                3         => '3',
                4         => '4',
            ],
            '#default_value' => $this->configuration['columnNum'],
            '#empty_option'  => t('-select-'),
            '#ajax'          => [
                'callback'      => [$this, 'columnCallback'],
                'wrapper'       => 'columns-wrapper', 
            ],
        ];
        $form['column'] = [
            '#type' => 'container',
            '#attributes' => ['id' => 'columns-wrapper'],
        ];
        for ($i = 0; $i < $columnNum; $i += 1) {
            $form['column'][$i] = [
                $i => [
                    '#type'       => 'details',
                    '#title'      => t('Column '.$numTitle),
                    '#open'       => FALSE,
                    'columnTitle' => [
                        '#type'      => 'textfield',
                        '#title'     => t('Column Title'),
                        '#value'     => $config[0]['columnTitle'],
                    ],  
                ],
            ];  
        return $form;
    }

In the callback we only need to return the ajax wrapper.

public function columnCallback(array&$form, FormStateInterface $form_state) {
    return $form['column'];
}

Drupal rebuilds the form on every ajax request and puts it in the parameter $form of the callback. It would make no sense to try to rebuild it again.

I guess you're missing wrapper method in your '#ajax' (next to callback) which consist the HTML id attribute of the area where the content returned by the callback should be placed. See: Ajax API. Then you've to make sure such container id exist.

Code example (simplified):

public function blockForm($form, FormStateInterface $form_state) {
    $form['wrapper'] = array(
        '#type' => 'container',
        '#attributes' => array('id' => 'data-wrapper'),
        );
    $form['wrapper']['columnNum'] = [
        '#title'   => t('Number of Columns'),
        '#type'    => 'select',
        '#options' => [1 => '1', 2 => '2'],
        '#default_value' => $this->configuration['columnNum'],
        '#ajax'          => [
            'callback'   => '::columnCallback',
            'wrapper'    => 'data-wrapper',
        ],
    ];
}
public function columnCallback(array &$form, FormStateInterface $form_state) {
    return $form['wrapper'];
}

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For complete code example, see: How to Add more option for type radios use Ajax in Drupal 8.