There is a new wage determination; however, neither the labor rate nor H&W has changed. Are we still required to do a modification to incorporate the new Wage Determination?
This is actually a really interesting question.
The FAR and DFARS are silent on your specific scenario. Typically you would follow the guidance at FAR 22.1007(b)(1) and there is also tangential guidance at FAR 22.1007(c) and FAR 22.1012-1(c). As a matter of common practice, most contracting organizations update the WD when they exercise the option regardless if the wage rates and fringes have changed.
I could also not find anything regarding your scenario when reviewing the DOL H&W division page and the new beta.sam.gov Wage Determinations Learning Center.
Therefore my recommendation is for you to contact your Service Labor Advisor; if you do not know who it is, the list (including phone and e-mail address) are located here: https://www.acq.osd.mil/dpap/cpic/cp/labor_information.html