yep - bart, brucella, rickettsia are all proteobacteria - there is a kind of family tree here that gives you an idea of how they are all related
https://www.researchgate.net/figure/evolutionary-distance-tree-of-representatives-of-the-alpha-subclass-of-the-proteobacteria_fig2_13990039that far from a complete family tree though - there are likely too many to display - and nomenclature / taxonomy of bacteria gets a bit messy as the groupings were often set up long before molecular techniques were invented - and scientists just had things like microscopes and dyes and what stuff the microbes ate and excreted as ways of telling which ones were similar - here is a summary of how the groups were set up - bart etc are in the alphaproteobacterial class - see the block diagram here
https://www.researchgate.net/figure/the-subgroups-of-proteobacteria-and-the-main-members-of-each-subgroup_fig1_232715029but in the real world later molecular methods demonstrated that it just doesn't always work like that - and so taxonomists are forever having to revise the names and relationships
incidentally the patient in the first paper was found to have a blood infection with something in this family of organisms - but one that had never been detected before - so i guess what the LLMD's say about
many strains and species of bugs - not all of them discovered - may well be true