If we do not specify a bibliography style, LaTeX export will fail.
With the attached patch, the following simple-minded Org document will
export without errors:

 #+title: Testing org-cite \LaTeX export
 #+latex_header: \usepackage{natbib}
 #+bibliography: bibliography.bib
 #+options: toc:nil
 #+cite_export: natbib

 Hello World! This is a citation: [cite:@citationkey2023]

 #+print_bibliography:

Also, should we provide some commonly available natbib styles in the
defcustom?