In those kinds of situations, you have a few different paths.
If you use button_to for the button with remote: true, you can make an AJAX call via RailsUJS to your Rails application which would be a JS format. Within the <action>.js.erb, you could render a partial and insert it onto the page. If that partial has a stimulus controller within it, the controller would initialize and "just work"
If you use a stimulus controller for the button, when clicked, you can make the AJAX request back to the Rails application in a similar fashion and then render a partial within the Rails controller action and then insert this into the page.