I have an art portfolio site in development.

I have used CPT UI to set up:
post type: works
taxonomy: mediums
mediums: paintings, etc

The best way I could think to set this up was to use taxonomy-medium.php as the archive/template for displaying these custom posts.

This is working fine with the following code:

    <?php if ($posts) : ?>
        <!-- Slider main container -->
        <div class="swiper mySwiper">
            <!-- Additional required wrapper -->
            <div class="swiper-wrapper">
                <!-- Slides -->
                <?php foreach ($posts as $post) :
                    setup_postdata($post) ?>
                    <div class="swiper-slide"><?php the_content(); ?></div>
                <?php endforeach; ?>
            </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 wp_reset_postdata(); ?>

    <?php endif; ?>

Now I want to clean up the UI by doing 2 things.
First, I would like to remove the custom taxonomy slug from urls, changing it from
https://site.dev/medium/paintings to https://site.dev/paintings
I've tried several plugins that claim to do this and none worked.

Next I would like to forego a landing page, and just have https://site.dev/paintings as the front page, showing the content from the archive page code shown above.

I have looked through many answers to both these questions, and have not been able to find a working solution. If I set a page with:

    <?php locate_template( 'taxonomy-medium.php', TRUE, TRUE ); ?>

it loads the slider but returns no posts. Ideally I would also like the home url to redirect to https://site.dev/paintings so that clicking on menu item paintings shows the same url.