When Does "Anastasia" (1952) Take Place?
"Anastasia" is a historical fiction stageplay written by Marcelle Maurette first performed 1952. So when is "Anastasia" set?
It takes place in the year:
We know this because it must have been some time since the Russian Revolution. The Russian Revolution happened in stages, starting in March of 1917 AD and then continuing in November of 1917 AD in the real world. So it must be after 1917 AD.

1926 AD
We know this because it must have been some time since the Russian Revolution. The Russian Revolution happened in stages, starting in March of 1917 AD and then continuing in November of 1917 AD in the real world. So it must be after 1917 AD.
Furthermore, Prince Arcade Arcadievitch Bounine claims, ..."I've seen the Empress. It's not likely her own memory is what it was. She's nearly 80." referring to the real-world Dowager Empress Marie Feodorovna who was born in 1847 AD and thus was in her late seventies from 1922 AD to 1926 AD. So it must be between 1922 AD and 1926 AD.
1847 + 75 = 1922
or
1847 + 79 = 1926.
More specifically, Bounine says, "I must remind you again that those 8 years would not have been what the first 16 were." presumably referring to the age Anna (loosely based on the real-world Grand Duchess Anastasia Nikolaevna) was if she is really Anastasia: born on June 18th, 1901 AD, 16-years-old when the Revolution came in 1917 AD, and 24-years-old in 'the present'.
6.1901 + 16 = 6.1917
and
6.1917 + 8 = 6.1925.
So it must be after June of 1925 AD and before June of 1926 AD, when she would turn 25.
The playbill for the original Broadway performances states the date at the beginning of act 1 is "January, 1926." So presumably it is January of 1926 AD.
Later, Piotr Constantinovitch Petrovin muses, "What she's managed to learn in one month–" and Boris Chernov corrects him "5 weeks." so we know only 5 weeks has passed since the start of the show and it's still within the 1926 AD calendar year.
Act 2 is labeled in the playbill as "One month later." so February of 1926 AD and act 3 is "Two weeks later." so presumably the play ends in late February of 1926 AD.
It has been adapted to film in 1956, as an audio-drama in 1982, to animation in 1997, and as a stage-musical in 2016.