Some suggestions:

• Connect taxonomy podcast_category to custom post type podcast
• Change the select form field name for orderby (if possible)
• Add (the newly named) orderby parameter to WP_Query for use as a filter
• Avoid query_posts()

Explanations and updated code samples are below.

Connect taxonomy podcast_category to custom post type podcast

WP Docs for register_post_type say that:

any taxonomy connections should be registered via the $taxonomies argument

When calling register_taxonomy() set the $object_type argument to null (see wordpress.stackexchange.com answer here), and use the 'taxonomies' property in the call to register_post_type() to connect the podcast_category taxonomy to the podcast custom post type. While there are other ways to accomplish the same thing, this approach is easy to understand.

Code in the podcast_custom_taxonomies() function would need to change from this:

    register_taxonomy('podcast_category', array('podcast'), $args);
}

…to this…

    register_taxonomy('podcast_category', null, $args);
}

Code in the podcast_custom_post_type() function would need to change from this:

            'revisions',
            'page-attributes'
        ),
    //'taxonomies' => array('category', 'post_tag'),
    'menu_position' => 10,
    'exclude_from_search' => false
    );

…to this…

            'revisions',
            'page-attributes'
        ),
    'taxonomies' => array('podcast_category', 'category', 'post_tag'),
    'menu_position' => 10,
    'exclude_from_search' => false
    );

Change the select form field name for orderby (if possible)

Using orderby as an argument in get_query_var() can cause problems. orderby is an existing WP_Query public query variable used to sort the list of posts. Your code seems to use orderby not as a sort key, but as a filter. When your code calls get_query_var('orderby') it is retrieving the existing WP_Query parameter value for orderby, not the value for orderby submitted by the HTML form.

The HTML form select options are podcast categories used as a filter. To reduce confusion, I suggest changing the HTML form select tag name and ID to podcast_category_filter.

Add (the newly named) orderby parameter to WP_Query for use as a filter

Assuming orderby has been changed to podcast_category_filter, the get_query_var() function can be called to get the value submitted by the HTML form only after the field podcast_category_filter has been added to the list of WP_Query public query variables. Once added to the list, WordPress will know that when it sees podcast_category_filter in the URL (e.g. https://example.com/podcast?podcast_category_filter=sports), podcast_category_filter and its value should be added to WP_Query. The value for podcast_category_filter can then be retrieved using get_query_var('podcast_category_filter').

To add podcast_category_filter to the list of WP_Query public query variables, use the query_vars filter hook in your theme or plugin:

function myplugin_query_vars( $qvars ) {
    $qvars[] = 'podcast_category_filter';
    return $qvars;
}
add_filter( 'query_vars', 'myplugin_query_vars' );

Avoid query_posts()

Please note this warning from the WordPress Docs on the use of the query_posts() function:

Note: This function will completely override the main query and isn’t intended for use by plugins or themes. Its overly-simplistic approach to modifying the main query can be problematic and should be avoided wherever possible. […] This must not be used within the WordPress Loop.

WordPress suggests using the pre_get_posts action within WP_Query.

To avoid query_posts() changes to your code could look like this:

Delete this from your theme page:

query_posts(array(
   'post_type' => 'podcast'
)); ?>

Update your pre_get_posts action hook to this:

add_action('pre_get_posts', 'altering_podcast_archive_query', 99);
function altering_podcast_archive_query($query)
{
    // You may wish to put this line within an if-statement if there are
    // conditions under which the post_type should not be filtered.
    $query->set('post_type', 'podcast');

    if (
        is_post_type_archive('podcast') 
        && 
        get_query_var( 'podcast_category_filter' )
       ) 
    {
        $tax_query = array(
            array(
                'taxonomy' => 'podcast_category',
                'field' => 'slug',
                'terms' => sanitize_text_field( get_query_var( 'podcast_category_filter' ) ),
            )
        );
        $query->set('tax_query', $tax_query);
    };
};

Alternative for creating form select HTML

If you don’t need special class names or custom attributes in the select or option tags consider using wp_dropdown_categories():

<?php
$selected_category_slug = get_query_var( 'podcast_category_filter' );

$args = array(
    'taxonomy'    => 'podcast_category',
    'selected'    => sanitize_text_field( $selected_category_slug ),
    'name'        => 'podcast_category_filter',
    'hide_empty'  => false,
    'value_field' => 'slug',
    'echo'        => false // Set to true to echo the HTML directly rather than save the HTML to a variable.
);
$select_category_html = wp_dropdown_categories( $args );
?>

<form method='GET'>
    <?php echo $select_category_html ?>
    <button type='submit'>Filter</button>
</form>