QuickBooks Online has its own Job costing feature, nena5. This functionality allows you to track expenses associated with specific jobs or projects.
However, this would require you to record the expenses in QBO so you can add them when invoicing your customers.
Since you're using a third-party app to track piece rates, I suggest reaching out to the app's developer to see if there's a way to sync Acculynx and QBO to import expenses into the program.
If not, other apps can also bridge Acculynx and QBO. You can find accredited apps in the QuickBooks App Store. Here's the link: https://quickbooks.intuit.com/app/apps/home/en-us/.
Please note that we're unable to associate other types of expenses for payroll reporting since QBO relies on time tracking for labor costs.
As a workaround, you can use the Projects feature within QBO to track time internally. Then, you can use the tracked hours so they will flow into your payroll reports when creating paychecks. This can help bridge the gap between piece rate tracking and the labor cost reporting in QuickBooks Online.
Let me share these articles for additional details in case you're interested in using this feature:
Lastly, I'd suggest sending feedback about being able to associate piece rates or billable expenses when running payroll in QBO. Here's an article on how to submit product suggestions: Give feedback on QuickBooks products and services.
Don't hesitate to ask follow-up questions or post new inquiries if you need anything else.