In chapter XX of John Murray's memoir, there is an exchange of correspondence between himself and the Marchioness of Abercorn, who had (like Jane and Henry Austen) enjoyed his largesse in the form of being sent the latest fruits of his press to read for free.

Unlike the Austens, it appears the Marchioness had been in the habit of sending the boring books back in exchange for more modish ones.
Murray jovially suggests holding back Rob Roy by Scott, and the latest canto of Childe Harold by Byron (these being the latest 'Harry Potters' of their day), lest Lord Abercorn find them indifferent, adding "You will be alarmed, I fear, at having provoked so many reasons for sending you dull
publications.... I am printing two short but very clever novels by poor Miss Austen, the author of 'Pride and Prejudice.'"

The Marchioness responds to this "Pray send us Miss Austen's novels the moment you can.".

It seems that the reviewers, like the Marchioness, were interested in the novels, but more so in the person of the novelist, too late. (I get a distinct impression that some of these early reviewers were only interested in pedalling the personal details of a Lady Authoress, that there is a certain triumph in the knowledge that this author is just a plain 'Jane' with no great title, and the consciousness of what a critic would be seen to be, if he were to mercilessly scourge an author already dead, the only real restraint for some of these.)

There are more, but most are merely notices of new works, and probably paid for by the publisher (as, no doubt, were some of her reviews - John Murray bankrolled the Quarterly Review, so Scott was very much obliged to him when the review of Emma came out, in an edition already three months late. It might also explain why Whatley was indulged with such a lengthy review of a book that was not at all a new publication, by 1821)

Edinburgh Magazine, May 1818

Gentlemans Magazine July 1818

British Critic March 1818