Currently in QBO (with Standard Payroll) there is no facility to tag auto-generated Payroll Journal entries with a Class. This is inconsistent with the basic methodology of tagging every transaction with a Class. Payroll generates many journal entries so it is a lot of work to edit each line manually to add a Class.
For me, it would be adequate to apply the same Class tag to all Payroll Journals. This could be specified in Accounts and Settings / Payroll / Journal Mapping.