the API’s new identifications endpoint doesn’t work in conjunction with a project id parameter. your project is a traditional project, but assuming observations at the Clifton Field Station (place_id 124570) will roughly approximate the observations in your project, then you could use that place_id in place of your project_id, like so:
otherwise, you’d have to basically compare recent observations vs all observations in the project. this is a slightly different methodology than the above because it’s based on new observations rather than new identifications – new identifications may be more useful if the observations in your set aren’t necessarily identified quickly – but a tool such as the “new species” tool mentioned here may help to make that kind of comparison: https://forum.inaturalist.org/t/several-external-tools-for-inat-data-by-kildor/19906.