Trouble inputting variable into WP query

Combining Petar’s function and Tiago’s shortened option syntax, this works:

In template:

//once, in header:
$i = 0;

//anytime I want to run the query:
$i++;
$cat_query = prefix_get_wp_query($i);
 while ( $cat_query->have_posts() ) {
  $cat_query->the_post();
  get_template_part( 'template-parts/posts/content', get_post_type() );
  wp_reset_postdata();
}

In functions:

function prefix_get_wp_query( $i ) {
 if ( $i > 0 ) { 
  $cat = "b4_settings_homepage_category_".$i;
  $sector = get_option($cat)[0];
 }
 $cat_args = [
  'post_type'      => $post_types,
  'posts_per_page' => 3,
  'fields'         => 'ids',
  'post__not_in'   => [ $feat_ids, $latest_ids, $trend_ids ],
  'tax_query'      => [
   'relation' => 'AND',
    [ 'taxonomy' => 'sector',
      'field'    => 'id',
      'terms'    => $sector
    ]
   ]
  ];
  return new WP_Query( $cat_args );
}

Thanks very much!!