WordPress becomes very user-unfriendly once you want to start manipulating the URLs in the way you describe.
It is possible, but requires custom code, which I cannot provide.
You may find this article a helpful starting point:
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The first part requires setting custom rewrite rules that includes some placeholder text when the post type is first registered, and the second part uses the post_type_link filter to dynamically replace that placeholder text with your custom taxonomy term.
In terms of how you would do the same using Toolset, what you need to know is that the post type is registered by Types (according to what you enter in Toolset > Post types) and you cannot set the rewrite argument as described in the article.
What you can do, though, is use the WordPress filter register_post_type_args to modify the arguments used to register the custom post type as described in the article, by adding code such as this to your theme's functions.php file (not in Toolset > Settings > Custom Code):
function tssupp_custom_rewrite($args, $post_type) {
$slug = 'project'; // Edit the slug of the post type
if ($post_type == $slug) {
$args['rewrite'] = array('slug' => $slug . '/%customtaxonomy%', 'with_front' => 1);
}
return $args;
}
add_filter('register_post_type_args', 'tssupp_custom_rewrite', 10, 2);
You would then be in a position to do something similar to what is described in the second part of the article.
If that is not something you are comfortable with, you would need to hire a developer to do it for you.