I'm planning on using the embedded Service Desk Widget, but I find that its not very customizable. As a comparison I've used tawk.to in the past and their embeddable widget comes with a bunch of methods allow your site to interact with it.
https://www.tawk.to/javascript-api/
This means you can hide the "?" button entirely and have a button on your site activate the form, or have your site do things depending on the users interaction with the widget. Is there anything like this for the Jira widget, or is there any plan to introduce it?