Your understanding is close, but the key point is you are not really trying to persist pxUrgencyAssign itself. You are trying to ensure that when the assignment is recreated, the new assignment is created with the correct driver value in pyUrgencyAssignAdjust, so that Pega calculates the right urgency for that assignment. pxUrgencyAssign is derived from pxUrgencyWork + pxUrgencyAssignSLA + pyUrgencyAssignAdjust, so the durable value to carry is the adjuster, not the final urgency
If the value is being set directly on newAssignPage, I would avoid that approach because newAssignPage is part of assignment creation processing and may not be the most reliable place to drive persisted urgency values. At assignment creation, copy that value into pyUrgencyAssignAdjust if you want it to affect the assignment’s urgency. Let Pega recalculate pxUrgencyAssign from the standard formula rather than setting pxUrgencyAssign directly.
compute the value you need in a property and use that to populate pyUrgencyAssignAdjust during assignment creation or the post processing of the current assignment before it is redirected to the same assignment for SLA computation., or you can also leverage the Assign-.NewDefaults activity which is invoked for every Assignment creation.