A footnote in the Norton edition of Persuasion suggests that Sir Walter was using the 1808 edition of Debrett's 'Baronetage of England'

I cannot find the text of this on-line, but another possibility is Bentham's "The Baronetage of England", published in five volumes 1801-05. Volume one is linked below this post.

Scroll down to 'Related Books' for links to several other 18th and early 19th century versions of the Baronetage, including volume 2 of Debrett's Baronetage (1815).

Scroll further down to 'Other Editions' for links to the remaining four volumes of Bentham (1802-1805).

I have linked to Bentham partly because the on-line text is complete. I had not looked at a Baronetage (or a Peerage) before, and one thing which struck me immediately is the insistence on the date when a Baronetcy was created. The rule is clear - oldest first - which of course creates the order of precedence in circles where such things matter. I think seeing the details and the age of his title set down in such a book would tend to reinforce Sir Walter's conviction that such things mattered very much indeed!

To most people today importance of the date when a baronetcy was created seems irrelevant and possibly absurd, and it seems that JA and most of her contemporaries would have thought so too. But precedence did matter them much more so than today, at least among the gentry - think of Lydia Bennet claiming her right to go into dinner ahead of her sisters once she was married, and Elizabeth Elliot "..walking immediately after Lady Russell out of all the drawing-rooms and dining-rooms in the country."

I found the Preface to Bentham's "Baronetage"(pages vii - xiv) quite interesting.
It's fawning tones and the description of the baronetage as "the stem of nobility" would have been balm to Sir Walter's impoverished soul. And consider the following passage:

"The genius, the virtues, and achievements of eminent men, ought to be remembered; and even those, who although not prominent in public affairs, or engaged in pursuits interesting to strangers, had in their private spheres demeaned themselves with propriety, and supported the line of an eminent family with respectability, ought not to be forgotten."

I wonder if seeing opinions like this in print would have reinforced Sir Walter's obsession with the importance of keeping up appearances.

The last pages (xii - xiii) of the Preface make the point that many recently created baronetcies were awarded to men from different spheres of society than had previously been the case. It goes on to state "..the urgent propriety of preserving every source of honour free from the contamination of unworthy members, or the depreciation arising from a great increase in there numbers..."