Pager includes a number of application-style interactions, including the tooltip descriptions that are attached to the list of page links. Testing it with NVDA, much of the descriptive richness of Pager isn't apparent until the user manually switches into Browse Mode. We don't include any instructions to the user about the need to do this.
However, since they'll also need to do this to interact with the data table, it seems reasonable to wrap the whole Pager container in an "application" role so that the mode-switching occurs automatically.
We'll need to test this with real screenreader users to verify that it is the best approach, but it seems like a reasonable starting point.