"can we print W-2s for them if they provide a backup of their Quickbooks if we no longer paid for our own Quickbooks payroll service?"

Whew; please note that I am not current on this stuff. The past few years, I've been working only as developer support and stopped teaching in 2015 (except one summer class) and stopped supporting end users in 2020 (this is my first year with no clients at all; I might be retired...).

It all works off of the key. When I got a client's file, it came with their payroll key active, or I put that in when setting up/fixing their file. There used to be Manual, Basic and Advanced Payroll, as well as Accountant's Payroll. The Accountant's Payroll had more functionality, including after-the-fact payroll. I supported a Pro Advisor where we would put in the Accountant's key to do the work the client didn't have at their subscription level. The Accountant's Payroll entitled you to use your key with 50 FEIN. I seem to recall that before you give back a client's file, you would remove your accountant key and put theirs back. Try this topic, to see if that helps at the least, describe some usage:

https://quickbooks.intuit.com/learn-support/en-us/employees-and-payroll/enhanced-payroll-for-account...

So, you should be able to use their file to do anything they have authorized and are paying for, which was always a bit scary to me. I never wanted to accidentally run their payroll or efile their pending PR liab payments or direct deposit, when simply trying to fix their payroll mistakes, such as Deductions the wrong type (gross or not) wrong additions (taxable or not), child support and other garnishments, etc.

If you were never using your key in their file, you never needed your own payroll subscription, in other words. You might need them to upgrade to Enhanced Payroll, though. Does that help?