Show custom category archive as front page and remove taxonomy slug from urls

I was able to solve this by removing CPT UI plugin, registering the custom post type with:

function create_post_type() {
  $args = array (
      'public' => true,
      'has_archive' => true,
      'show_ui' => true,
      'supports' => array('revision','title','editor','author', 'thumbnail', 'custom-fields'),
      'taxonomies'          => array( 'category' ),
      'labels' => array(
        'name' => __( 'work' ),
        'singular_name' => __( 'work' )
      )
  );
  register_post_type('work', $args);
}

Then in category.php:

<?php get_header();

    $args = array(
        'post_type' => 'work',
        'cat' => get_query_var('cat'),
        'posts_per_page' => -1 );

    $loop = new WP_Query( $args ); ?>

    <!-- Slider main container -->
    <div class="swiper mySwiper">
        <!-- Additional required wrapper -->
        <div class="swiper-wrapper">
            <!-- Slides -->
            <?php while ( $loop->have_posts() ) : $loop->the_post(); ?>
                <div class="swiper-slide"><?php the_content(); ?></div>
            <?php endwhile; ?>
        </div>
    </div>

    <!-- If we need pagination -->
    <div class="swiper-pagination"></div>

    <!-- If we need navigation buttons -->
    <div class="swiper-button-prev"></div>
    <div class="swiper-button-next"></div>

<?php
// get_sidebar();
get_footer();

It wasn’t immediately intuitive that ‘cat’ needed to be specified to filter results by the current category, and not have all posts returned.

For now I’m using a plugin ‘Remove Taxonomy Slug’ to change the url from /category/name to /name

It seemed unnecessarily difficult to have the homepage be a specific category archive (from category.php) so I’m showing the About page instead.