Add “All Posts” button to custom post taxonomy filter with ajax in wordpress

I updated your code there is 2-3 mistake in js file datatype and function file query parameter.
Below I paste an updated code, please check and let me know incase of any doubts.

Your album-page.php

<?php
$args = array(
    'post_type' => 'albums',//Custom Post type name
    'posts_per_page' => 10,
);

$query = new WP_Query($args);

$tax = 'album_category';//Custom post type taxonomy name
$terms = get_terms($tax);
$count = count($terms);

if ($count > 0):
    ?>
    <div class="post-tags">
        <?php
        echo '<a href="#" class="tax-filter" title="">All</a> ';
        foreach ($terms as $term) {
            $term_link = get_term_link($term, $tax);
            echo '<a href="' . $term_link . '" class="tax-filter" title="' . $term->slug . '">' . $term->name . '</a> ';
        }
        ?>
    </div>
<?php
endif;
if ($query->have_posts()):
    ?>
    <div class="tagged-posts">
    <?php while ($query->have_posts()) : $query->the_post(); ?>

            <h2><a href="https://wordpress.stackexchange.com/questions/355730/<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>
            <?php the_excerpt(); ?>

    <?php endwhile; ?>
    </div>

<?php else: ?>
    <div class="tagged-posts">
        <h2>No posts found</h2>
    </div>
<?php
endif;
wp_reset_postdata();
?>

Your functions.php

function ajax_filter_posts_scripts() {
    // Enqueue script
    wp_enqueue_script('jquery');
    wp_register_script('afp_script', get_template_directory_uri() . '/assets/src/js/ajax-filter-posts.js', 'jquery', null, true);
    wp_enqueue_script('afp_script');

    wp_localize_script( 'afp_script', 'afp_vars', array(
          'afp_nonce' => wp_create_nonce( 'afp_nonce' ), // Create nonce which we later will use to verify AJAX request
          'afp_ajax_url' => admin_url( 'admin-ajax.php' ),
        )
    );
  }
  add_action('wp_enqueue_scripts', 'ajax_filter_posts_scripts', 100);
// Script for getting posts
function ajax_filter_get_posts($taxonomy) {
    // Verify nonce
    if (!isset($_POST['afp_nonce']) || !wp_verify_nonce($_POST['afp_nonce'], 'afp_nonce'))
        die('Permission denied');
    $taxonomy = $_POST['taxonomy'];
    // WP Query
    $args = array(
        'post_type' => 'albums',//Custom Post type name
        'posts_per_page' => -1,
    );
    if (!empty($taxonomy)) {
        $args['tax_query'] = array(
            array(
                'taxonomy' => 'album_category',//Custom post type taxonomy name
                'field' => 'slug',
                'terms' => $taxonomy,
            ),
        );
    }
    $query = new WP_Query($args);
    if ($query->have_posts()) :
    ?>
    <div class="tagged-posts">
        <?php while ($query->have_posts()) : $query->the_post(); ?>

            <h2><a href="https://wordpress.stackexchange.com/questions/355730/<?php the_permalink(); ?>"><?php the_title(); ?></a></h2>
            <?php the_excerpt(); ?>

        <?php endwhile; ?>
    </div>
    <?php
    endif;
    wp_reset_postdata();
    die();
}
add_action('wp_ajax_filter_posts', 'ajax_filter_get_posts');
add_action('wp_ajax_nopriv_filter_posts', 'ajax_filter_get_posts');

Your ajax.js

jQuery('.tax-filter').click(function (event) {
        // Prevent defualt action - opening tag page
        if (event.preventDefault) {
            event.preventDefault();
        } else {
            event.returnValue = false;
        }
        // Get tag slug from title attirbute
        var selecetd_taxonomy = $(this).attr('title');
        $('.tagged-posts').fadeOut();
        var data = {
            action: 'filter_posts',
            afp_nonce: afp_vars.afp_nonce,
            taxonomy: selecetd_taxonomy,
        };
        $.ajax({
            type: 'post',
            dataType: 'html',//Return type is html
            url: afp_vars.ajaxurl,
            data: data,
            success: function (data, textStatus, XMLHttpRequest) {
                $('.tagged-posts').html(data);
                $('.tagged-posts').fadeIn();
                console.log(textStatus);
                console.log(XMLHttpRequest);
            },
            error: function (MLHttpRequest, textStatus, errorThrown) {
                console.log(MLHttpRequest);
                console.log(textStatus);
                console.log(errorThrown);
                $('.tagged-posts').html('No posts found');
                $('.tagged-posts').fadeIn();
            }
        })

    });

Thanks.