I see that Dynamic have issued this follow-up to their 2013 release of Kalkbrenner's Op1 with Luigi Gerosa. This hopefully suggests that they may be going to complete a Kalkbrenner sonata cycle - certainly the later examples are more interesting!
Audio samples here:
https://www.jpc.de/jpcng/classic/detail/-/art/3-klaviersonaten-op-4/hnum/7567826 (https://www.jpc.de/jpcng/classic/detail/-/art/3-klaviersonaten-op-4/hnum/7567826)