The title says ‘delete button’ and in the details you mention ‘cancel button’
All depends on what has been configured as action for the button. By default delete would delete the record and because at that time the object does not exist anymore, all other buttons requiring that object to exist (eg save) will not work anymore. Similar case for cancel. If you cancel after creating the object, the object does not exist anymore and the buttons will not work.
You may want to look into refresh and close page settings for the buttons, or you would have to construct a microflow to take care of all required action.
Hope this helps