As I know - as Catharine the Great succeed the throne she made sure that any positives of Peter III deeds are disappeared. She wrote her own memoir where she showed all details of palace life and showing Peter III as a nitwit. Her variant of "history" was supported with Russian historians.
At one time Roman orator Cicero in his speech against corrupt governor said that all his rich villas are "silently screaming" about their owner's crimes. And buildings that were built during Peter III running "silently scream" that their owner was not a drunk monster and stupid soldier. I'm talking about Opera theatre in Concert Hall an Oranienbaum (Peter III's official residence not far from St Petersburg). Under his personal order the school for serf's kids was opened . A lot of famous Russian artists graduated this school (dancers, musicians, singers and composers).
Peter III indeed played with toys - but they were soldiers toys and and (the most importantly)- the military education, including construction and attacking of different kind of fortifications were the part of upbringing program of any prince in XVIII century.
There is no doubt that Catharine II was the great ruler and during her running Russian Empire had it's golden century. All I'm trying to say that with any emperor/ess also had their good deeds - some of them more some of them less.