How to check if a referenced entity is being used in other places?
Is there a quick way to check if a paragraph (or any entity) is being
  used and in which places (preferably one that shows paths) so that I
  can remove the reference before deleting this paragraph reference
  option from my paragraph component?


A paragraph can only be used in one place. So I'm first answering the part "or any entity", which also reflects the question title, and address the paragraphs specifics later.

I would do this in two steps. First find all entity reference fields which are configured to target this entity type, then run an entity query for each field.

As example how to find all entities where term #1 is used:

use Drupal\field\Entity\FieldStorageConfig;

$target_id = '1';
$target_type = 'taxonomy_term';

$map = \Drupal::service('entity_field.manager')-&gt;getFieldMapByFieldType('entity_reference');
$results = [];
foreach ($map as $entity_type =&gt; $fields) {
  foreach ($fields as $field_name =&gt; $field) {
    // we are only interested in configured fields, not base fields
    $config = FieldStorageConfig::loadByName($entity_type, $field_name);
    if ($config &amp;&amp; $config-&gt;getSetting('target_type') == $target_type) {
      $ids = \Drupal::entityQuery($entity_type)
        -&gt;condition($field_name, $target_id)
        -&gt;execute();
      $results[$entity_type][$field_name] = $ids;
    }
  }
}


If the field is configured in a paragraph type, the IDs you find are of paragraph entities. Load the paragraph and get the parent entity with $paragraph-&gt;getParentEntity(). For nested paragraphs do this multiple times, until you find a non paragraph entity, for example a node.