Battlecruisers were pratically descontinued after WW1.
Pretty fair. Thats an afterknowledge tho, the fate of battlecruisers can not be known at the date this ship was designed, but its up to you.
The principal reason was almost all major navies left WW1 with lots of cruisers with France exception.
This is the secondary reason. If this technology was really possible in late WW1, we would see Frobishers and Emeralds with turrets and Omahas with superfiring layout. However, no cruisers had superfiring layout until Duguay-Trouin.
For example, one of the very first US cruiser designs with superfiring layout is dated 1923 - Design 292, 11 500 tons of displacement, 4x2 203 mm guns (source - Norman Friedman's book "US Cruisers - Illustrated design history, page 119). I am absolutely sure that for other nations this date is relevant too - Counties appeared in 1928, Leanders - in 1929. German Emden was built in 1925 and had no turrets at all.
Ersatz Sharnhorst is pratically a heavy cruiser with a little more armour than usual. It's a technological possibility in WW1 universe.
I dont say this is impossible, I respoded to statement "heavy cruiser outlived the armored cruiser" that is a bit wrong. Armored cruisers and pre-dreadnoughts were "pair" pretty much as battlecruisers and dreadnoughts. Heavy cruisers (thanks to Washington) were limited and thus served for different roles (BCs in dreadnought era and ACRs in pre-dreadnought era could be used for charging retreating battlefleet, for example - a thing that CA cant do for obvious reasons).
Yes, but battlecruisers were a lot more costly
Yes, but much more effective and suitable in that time period. Heavy cruiser feels herself incomfortable outside the Washington era because in that time she simply cant be faster than a battlecruiser (because yeah, technology level - no way you can be faster then HMS Princess Royal built 1911, for example, with her 28 kts - this will require a massive and expensive machinery; Later Renowns with 32 kts are an absolute instant death), therefore helpless in a fleet battle (just like Blucher) - cant fight, cant run. Heavy cruiser of WNT era can easily escape from larger enemies - because advancements in turbine technology made during years after WW1 allowed to produce small and powerful engines.
All other surviving heavy cruisers were obsolete and in disrepair condition.
But you said that heavy cruisers were used well after WW2?
Ersatz Scharnhorst's could be useful as raiders and scouts.
I mean, yes, she can be deployed for foreign station and can be succesful, since she is a relatively fast an powerful ship. But she cant pursuit lighter cruisers because she is too slow (Arethusas of 1913 are capable of ~29 kts) and battlecruisers are too deadly.
I dont want to say, however, that the design itself is bad, no-no. My point is that she is a bit off her era - she uses doctrines of ~1920s and ideas of ~1910s which is somewhat strange to see in WW1. German Empire already was in a harsh conditions and it is very unlikely to see her returning to ideas of an armored cruiser.
But well, this is an alternate universe where everything may happen. Ersatz Scharnhorst is certainly a nice looking ship and that 1929 Blucher is even better (at least to my taste). Best wishes in further drawing