Pravoslavac,
Actually, St. Peter’s was “assigned” or “dedicated” to
THE LATIN patriarch of Constantinople–not the EO one. The Latin patriarch was installed after the fourth crusade as a rival or replacement for the EO patriarch, but was ejected from Constantinople in 1261, and “reigned” hundreds of miles away at St. Peter’s.
St. Peter’s a Latin church, long under the guidance of a Latin patriarch. The thought that one could claim St. Peter’s for Eastern Orthodoxy is (honestly) ridiculous. You keep Hagia Sofia, we’ll keep St. Peters, lol. Thank you.

(Though technically, Hagia Sofia is a legacy of the undivided Church.)
P.S. St. Peter’s dome was modeled on the Pantheon’s dome (an ancient Roman temple, later converted into a Latin church)–not an “EO style.”