Approval field updates re-entering the save order
Key Takeaway
An approval field update doesn't trigger workflow rules on its own. If you select "Re-evaluate Workflow Rules After Field Change" on that field update and it changes the field's value, Salesforce reevaluates the workflow rules on the object and fires any rule whose criteria are now met.
A field update action automatically sets a field's value. A classic approval process can use field update actions just as a workflow rule can. An approval field update doesn't set off every automation on the record, so other automation might not run after an approval step changes a field. The Re-evaluate Workflow Rules After Field Change setting lets an approval field update send the record back through workflow rule evaluation on the same object.
Field update actions
A field update action automatically sets a field's value. You can attach field updates to workflow rules, approval processes, or entitlement processes. Salesforce recommends designing automated actions so they work for both workflow rules and approval processes.
Field updates work independently of field-level security. A field update can therefore change a field that is hidden on the user's page layout.
Within a set of actions, field updates run after case assignment, lead assignment, and auto-response rules. They run before email alerts, tasks, and outbound messages.
Avoid giving a rule or approval process more than one field update that sets different values on the same field. When a single workflow rule has multiple field updates like that, the result is unpredictable.