Current behavior:
It is not possible to update the Time Spent field using Automation for Jira. When we log time while working on the issue, we do not have a way to automatically add this value to "Time Spent" field during transition.

Expected behaviour:
It would be great to have the ability to automatically add the logged time to "Time Spent" field during transition.

Workaround:
Create an Automation rule that triggers when work hours are logged on an issue. The rule should edit a text field with {{issue.timetracking.timespent}} smart value. Add this field just above the Log Work field on the transition screen.

What this will do:
When any user updates the work hours on an issue, this field will show the total work hours logged.
As the Text type field and the Time Spent field are both on the same screen, user can copy the data directly while resolving the issue.

Note: The rule will consume execution as per this document.