When a spire encounter is opened, it's a option to mouse over the chest to find out what the possible prizes are. Within the open encounter panel, the number of spirit essence that will be received for success is also displayed.
When outside of an encounter window, it is an option to mouse over chests/encounters that have not yet been reached and the tooltip displays the possible prizes for that chest. Would it also be possible for that tooltip to also display the spirit essence count for that encounter? Would make it easier to work out how many more are required to reach a particular goal for spirit essence.