Source code for https://formidable-masterminds.com/add-new-create-post-action-taxonomy/

function-complete.php

<?php

add_action( 'frm_after_create_entry', 'create_new_cpt_taxonomy', 30, 2 );
function create_new_cpt_taxonomy( $entry_id, $form_id ) {

	/* first thing to do is to make sure this runs on the correct form */
	if( $form_id == 32 ) { //change 32 to the ID of your form

		if( isset( $_POST['item_meta'][254] ) ) { //change 254 to the ID of the field used to add a category

			$taxonomy = 'city'; //if you're using a custom taxonomy, change this to the correct name
			$term = $_POST['item_meta'][254];

			/* first retrieve the entry object */
			$entry = FrmEntry::getOne( $entry_id );

			/* if there's no post_id, exit the function. There's nothing for us to do */
			if ( ! $entry->post_id ) {
				return;
			} else {
				/* make the association */
				wp_set_object_terms( $entry->post_id, $term, $taxonomy, true );
			}
		}
	}
}

multi-form-process.php

<?php

add_action( 'frm_after_create_entry', 'create_new_cpt_taxonomy', 30, 2 );
function create_new_cpt_taxonomy( $entry_id, $form_id ) {
	
	switch( $form_id ) {
		case 32 :
			if( isset( $_POST['item_meta'][254] ) ) {
				$term = $_POST['item_meta'][254];
				$taxonomy = 'city';
				process_new_cpt_taxonomy( $entry_id, $taxonomy, $term );
			}
			break;
			
		case xx : // second form id
			if( isset( $_POST['item_meta'][xxx] ) ) {
				$term = $_POST['item_meta'][xxx];
				$taxonomy = 'city';
				process_new_cpt_taxonomy( $entry_id, $taxonomy, $term );
			}
			break;

	}
}

function process_new_cpt_taxonomy( $entry_id, $taxonomy, $term ) {
	/* first retrieve the entry object */
	$entry = FrmEntry::getOne( $entry_id );

	/* if there's no post_id, exit the function. There's nothing for us to do */
	if ( ! $entry->post_id ) {
		return;
	} else {
		/* make the association */
		wp_set_object_terms( $entry->post_id, $term, $taxonomy, true );
	}
}