Although the authorship of the letters might be well known by 1809 - Southey had gone to some trouble to conceal his identity as the author, claiming that his hope was "that it may pass unknown through the hands of those Reviewers who are sure to detract from whatever is mine" and complaining that these Reviewers were too politically partisan in their opinions. (But it might also have been to evade going to gaol for seditious libel, as other Radical writers did.)

I wonder if Jane Austen is basing her opinions on the writing itself (showing her professional abilities in detecting the true author in its style with such certainty) or if she is being politically partisan: in 1807 Southey not only published the Letters, but on the recommendation of Sir Walter Scott, accepted the office of Poet Laureate and a small stipend of about £100 (Scott was turning the role down himself, because the stipend was very small, and it would oblige him to give up other more lucrative avenues for his writing - very clever).
Southey became a Tory overnight, and a Reviewer every bit as partisan as those he complained about, but the alteration of his opinions did not change his literary style. I wonder if Jane Austen's opinion of him would have changed?