There are no page templates in New Sites like Announcements, File Cabinet and List that are available in Classic Sites.
A workaround for File Cabinet is to upload the desired files to a folder in Google Drive, share the folder publicly and embed it in a page. See some examples here.
A file cabinet page when migrated to a New Site will not be automatically shared. Google developers say it is not possible to make the new file folder automatically shared.
See the "Site structure and page types" section here:
An example of a migrated file cabinet page is here:
A workaround for Announcement Page is to use a group like here.