There is a much more direct causal link as auto-immunity has been implicated in AD progression for years, e.g. [1-11]. I can't find the paper right now, but I once saw a very compelling longitudinal study where they regularly measured cognitive performance as well as several immunity markers in older subjects. Basically, every transient increase in antibody levels (IIRC, but they may have been tracking some other marker of immune system activation) was followed by a step decline in cognitive performance.
[1] Lopez (1991) Serum auto-antibodies in Alzheimer's disease
[2] Aisen (1996) Inflammation and Alzheimer disease
[3] D'Andrea (2005) Add Alzheimer’s disease to the list of autoimmune diseases
[4] Carter (2010) Alzheimer's Disease: A Pathogenetic Autoimmune Disorder Caused by Herpes Simplex in a Gene-Dependent Manner
[5] Reddi et al (2011) Autoimmunity in Alzheimer’s disease: increased levels of circulating IgGs binding Aβ and RAGE peptides
[6] Sardi et al (2011) Alzheimer's disease, autoimmunity and inflammation. The good, the bad and the ugly
[7] Marchese (2013) Autoimmune Manifestations in the 3xTg-AD Model of Alzheimer's Disease
[8] Li et al. (2018) Dementia and Alzheimer's disease risks in patients with autoimmune disorders
[9] Arshavski (2020) Alzheimer’s Disease: From Amyloid to Autoimmune Hypothesis
[10] Itzhaki et al (2020) Do infections have a role in the pathogenesis of Alzheimer disease?
[11] Lim et al (2020) Alzheimer Disease Pathogenesis: The Role of Autoimmunity