Apologies if this has already been posted somewhere but I haven't seen it so....
Looks like St. Peter's finally has a much better website than the former version!
https://www.basilicasanpietro.va/en.html
Lots of info on the site including hours, dress rules, available tours, background on the structure and its individual parts, etc. It does not include info or ticketing for the Vatican Museums; the link for that website is provided at the bottom of every page of the basilica's shiny new site.