Catherine would not have encountered Mirovich on her visit to Shlisselburg as he was not assigned there in 1762.
Potemkin was not a lieutenant in the Imperial Guard in 1762. By the time Catherine was placed on the throne, he had attained the rank of Kamer-Junker ("Groom of the Chamber").
Although Catherine did speak openly for the abolition of serfdom, according to Robert K. Massie's biography, she owned 500,000 serfs.
In real life, Paul was 8 years old when Catherine came to the throne, and way-too young to be a party to Mirovich's machinations.
Paul's coming of age was not celebrated nearly as lavishly as shown as Catherine was terrified of threats to her throne, and wanted to distract from him being her heir. Moreover, Potemkin arriving late to the party, saying "I'm sorry", then sitting down like nothing happened would have been unthinkable.