To update the Last Order Date custom field on the related account when an order is marked complete in Salesforce, the best practice is to use a record-triggered flow:
Create a Record-Triggered Flow:
Use Salesforce Flow to create a record-triggered flow on the Order object.
Set the flow to trigger when a record is updated (specifically, when the order status is updated to complete).
Update the Related Account:
In the flow, use a Get Records element to fetch the related Account record.
Use an Update Records element to update the Last Order Date custom field on the related Account with the date the order was marked complete.
This approach ensures that the data remains within Salesforce and is updated immediately as part of the same transaction, providing a robust and efficient solution.
Salesforce Flow Builder Documentation

To automate a workflow that requires data transfer between two Salesforce orgs and a distinct multi-user workflow within one of the orgs, the following tools are recommended:
MuleSoft Composer:
MuleSoft Composer allows for easy and quick integration between multiple systems, including different Salesforce orgs. It provides a no-code solution for connecting and syncing data across Salesforce instances.
Use MuleSoft Composer to create the integration flows that handle the data transfer between the two Salesforce orgs.
Flow Orchestration:
Salesforce Flow Orchestration is ideal for automating complex, multi-step business processes involving multiple users within a single org.
Use Flow Orchestration to design and automate the distinct multi-user workflow within one of the Salesforce orgs. It helps in coordinating user tasks, approvals, and other business processes seamlessly.
Combining these two tools leverages their strengths to handle both the integration and the complex workflow automation efficiently.
Salesforce Flow Orchestration Documentation
MuleSoft Composer Documentation