Not addressing the underlying cause of course but by reducing inflammation associated with autoimmune diseases such as rheumatoid arthritis or lupus. It's a little bit garbled but as far as I can tell baking soda appears to reduce inflammation by inducing the cholinergic anti-inflammatory pathway directly via mesothelial spleen cells rather than via the vagal nerve. https://eurekalert.org/pub_releases/2018-04/mcog-dbs042418.php
The paper in the Journal of Immunology referred to in the above press release is here: http://www.jimmunol.org/content/early/2018/04/14/jimmunol.1701605 Oral NaHCO3 Activates a Splenic Anti-Inflammatory Pathway: Evidence That Cholinergic Signals Are Transmitted via Mesothelial Cells Sarah C. Ray, Paul M. O’Connor et al. (long list of authors from Augusta University, Georgia.) J Immunol April 16, 2018
Q. Do we have to drink the baking soda, or can we ingest it in the form of cakes, scones, soda bread etc?
If you read the press release carefully, it becomes clear that the actual research being talked about was in healthy rats. The stuff about humans and autoimmune diseases was mention of other research that may be related to the effect found in the rats. This sentence in the article: Has somehow morphed into a title: which is not what the research was about. I agree, the press release, especially its title, is very misleading.