The show describes itself as "an occasionally true story" and inherently "anti-historical," meaning that while some of the characters are based on real-life people, they likely weren't very similar to their on-screen counterparts.
For example, while it's true that Catherine was married to Peter and did overthrow him, he died almost immediately after the coup and, while it's never been confirmed, was almost certainly assassinated.
Much like McNamara's The Favourite, what makes The Great special is that it, at almost no point, tries to pass itself off as a true story. It flies in the face of that and, while it's a gamble, that creative decision works incredibly well.
Allowing Nicholas Hoult's Peter to survive the overthrow and continue to be a character on the show is perhaps the wisest decision because he is so damn good in the role. He and Elle Fanning both steal every single scene they are in, whether they're on-screen together or not.
Its almost strict adherence to this policy of being anti-historical is how and why the show flourishes.
In real life, Catherine was responsible for ushering in Russia's golden age and helped make it one of the great powers of Europe. While the show has not caught up to that just yet (and it may not, as season 3 has not been confirmed), it's clear that the narrative is headed in that direction.
In the same vein as 2017's brilliant dark comedy The Death of Stalin, the characters, while supposed to be Russian, do not attempt accents or even pass themselves off as Russians. If they were making a strictly historical show with a dash of creative license, this might be an issue, but it isn't here.
Why? Well, the show isn't trying to be, and in many ways, wants to make sure you know that.