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The library view that you posted is dated 1826, therefore the room cannot be in the New Hermitage built in the 1840s-1850s. Moreover, I've a strong feeling that it doesn't exist anymore. The Winter Palace/Hermitage complex was rebuilt several times, including after the 1837 great fire, during which a library was known to have perished. Probably it was that same library pictured by Alexei Tyranov.