pxUrgencyAssign is a derived value, so when the SLA runs and creates newAssignPage, you can see the calculated urgency on that page, but that does not mean it will persist automatically to the database. In your case, repeatedly recreating the assignment page is causing the value to be recalculated in memory, but the underlying assignment record is not being updated in the way you expect
Also, changing pyUrgencyWorkAdjust will affect case urgency first, and because assignment urgency is derived from case urgency plus assignment components, the urgency change carries forward into other assignments. That is expected behaviour and is exactly why this property is not a clean way to make only one assignment behave differently.
In this scenario, the ticket is recreating a new assignment each time, so the issue is that the accumulated pyUrgencyAssignAdjust is not being carried forward. I think the safer approach is to persist the running increment on the case, e.g. in a dedicated property, and then reapply that value when the new assignment is created. That way the assignment can be recreated as many times as needed, but the accumulated assignment-specific urgency is preserved which would also affect case urgency and future assignments.