Hello,
Rick's book says to use the vaticanstate.va website to book a time and spot. That web site will send you to the museivaticani.va website, which does not mention a St. Peter's ticket. All Vatican related.
I did find a website called https://www.basilicasanpietro.va that states it is the "official" site to book your visit to the basilica. Is this where I book s time for a St. Peter's visit plus dome climb reliably?? Thank You!! Scammers beware...it looks official.