Increase the page size of the WordPress REST API

You cannot get over that limit of 100 posts per requests in WordPress for default requests. One way to still retrieve all posts would be to query that interface until you have all posts. Another would be a custom endpoint.

If you can, I suggest creating your own REST endpoint. This will already work and return all posts

add_action('rest_api_init', 'my_more_posts');

function my_more_posts() {
    register_rest_route('myplugin/v1', '/myposts', array(
        'methods' => 'GET',
        'callback' => 'my_more_posts_callback',
    ));
}

function my_more_posts_callback( WP_REST_Request $request ) {
    $args = array(
        'posts_per_page' => -1,
    );
    return get_posts($args);
}

More info on creating your own endpoint can be found here, whereas the arguments of get_posts() are explained here.

---

For a pure JavaScript solution in the frontend, you can utilize the x-wp-totalpages header which tells the total amount of pages. Unless this page is reached, we know we need to query again. So a basic recursive version like this works:

var allPosts = [];

function retrievePosts(opt) {
  if (typeof opt === 'undefined')
    opt = {};

  var options = $.extend({
    per_page: 100,
    page: 1
  }, opt);
  var url="https://example.com/wp-json/wp/v2/posts";
  var uri = url + '?per_page=" + options.per_page + "&page=" + options.page;

  $.getJSON(uri, function(data, status, jqXHR) {
    var totalpages = jqXHR.getResponseHeader("x-wp-totalpages');

    allPosts = allPosts.concat( data );

    // here the magic happens
    // if we are not done
    if (options.page < totalpages) {
      // request again, but for the next page
      retrievePosts({
        per_page: options.per_page,
        page: options.page + 1
      });
    } else {

      // WE ARE DONE
      // posts are in allPosts

    }
  });
};
retrievePosts();