Phylum Pseudomonadota has been published in this article. It is the correct and valid name and should be used, though the old taxa names tend to stick for a long time.
Article Valid publication of the names of forty-two phyla of prokaryotes
A great resource for bacterial taxonomy is LPSN by the german culture collection DSMZ.
Phylum Pseudomonadota is indeed validly proposed but it will take some time until taxonomy databases change this accordingly. For instance: SILVA latest upgrade 138.1 was before this change https://www.arb-silva.de/browser/ RDP https://rdp.cme.msu.edu/hierarchy/hierarchy_browser.jsp?qvector=136&depth=0&openNode=0&seqid=¤tRoot=0&searchStr=pseudomonas&endDataValue=&showOpt= and NCBI https://www.ncbi.nlm.nih.gov/Taxonomy/Browser/wwwtax.cgi?mode=Info&id=286&lvl=3&lin=f&keep=1&srchmode=1&unlock are not upgraded, also not the Genome Taxonomy database https://gtdb.ecogenomic.org/searches?s=al&q=pseudomonas but the source LPSN taxonomy already is: https://lpsn.dsmz.de/phylum/pseudomonadota
I recommend you to consult berjey's manual and prokaryot books. Pseudomonas is under proteobacteria group and now are considered as an ordre not a genre or species