Using WP_Query, I want to show posts that are associated with a custom taxonomy term

Your tax query should be an array of arrays.

Important Note: tax_query takes an array of tax query arguments arrays
(it takes an array of arrays). This construct allows you to query
multiple taxonomies by using the relation parameter in the first
(outer) array to describe the boolean relationship between the
taxonomy arrays.

https://codex.wordpress.org/Class_Reference/WP_Query#Taxonomy_Parameters

'tax_query' => array(
  // second array
    array(
      'taxonomy' => 'event-categories',
      'field'    => 'slug', 
      'terms' => $termst
    )
  // end second array
  ),

Second, the “key” is terms not term as you have it.