Does the word staff need to be pluralized if listing more than one person?

No, "staff" covers however many individuals there are.

The plural form "staffs" is used for two or more groups of employees.

Example: The staffs of the local merchants raised the funds for the park.

The noun "staff" (staffs) is also a Word for types of sticks or canes.

Example: The flags were shredded in the storm but their staffs were left intact.