After a conversation with ZD support I was asked to leave a little note here about my request.
We would very much like the ability to customise the UI of the Zendesk page, allowing us to move the messaging, notifications and call positions for a more optimal display. Often having these apps open can block content, or be blocked themselves and moving positions would be a game changer, and allow a more personalised experience for our agents.
Thank you for taking the time to provide us with your feedback. This has been logged for our PM team to review. For others who may be interested in this feature request, please add your support by upvoting this post and/or adding your use case to the comments below. Thank you again!