BramdeVriesProject for the Web (P3 & P5 licenses) https://docs.microsoft.com/en-us/office365/servicedescriptions/project-online-service-description/project-web-service-description#feature-availability which are apparently https://docs.microsoft.com/en-us/office365/servicedescriptions/project-online-service-description/project-web-service-description#feature-availability.
That said, whether the Resource Scheduling App 'works' is another question. There are significant issues with https://docs.microsoft.com/en-us/project-for-the-web/overview-universal-resource-scheduling#update-permissionsprivileges in the app and the disparate documentation across PSA, Field, Service product docs with little to none outlining the specific differences in functionality for P4W-only users.
So yeah its a mess but you can give it a try and hopefully some clear guidance docs for PW4-only use of URS app will come out at some point.
Until then your mileage may vary.
FWIW, we gave up on it after several support cases lasting months essentially resulted in https://docs.microsoft.com/en-us/project-for-the-web/overview-universal-resource-scheduling which - to say the least - leaves a lot to be desired.
HTH,
Josh