Exclude category when displaying all categories assigned to a post

get_the_category() has a filter, get_the_categories, that will filter the categories. You can do something like this:

add_filter( 'get_the_categories', 'wpse426499_filter_categories' );
/**
 * Filters the categories.
 *
 * @param  WP_Term[] $categories An array of WP_Term (ie, category) objects.
 * @return WP_Term[]             The filtered array of WP_Term objects.
 */
function wpse426499_filter_categories( $categories ) {
    $undesired_id = 2; // Set this to the ID of the category you want to exclude.
    // New array for the category objects.
    $filtered = array();
    foreach ( $categories as $cat_obj ) {
        if ( $cat_obj->term_id != $undesired_id ) {
            // If this isn't the unwanted category, add it to the array.
            $filtered[] = $cat_obj;
        }
    }
    // Return the array.
    return $filtered;
}

You can put this code in the functions.php file of your active theme, or — if you’re thinking of changing themes at some point — you can make it into a plugin.