I will look at this as if it was an rebuild from the original plans of the bismarck in modern times. still somewhat stupid, but not impossible, like what you are describing here.
first of all, the powerplant. you have 2 Davidson Nuclear engines. what do you mean with Nuclear engines? I would suppose you mean nuclear reactors and did not mention the affiliated steam turbines.
the old bismarck could go 30,1 knots on her 12 wagner boilers and her 3 brown-boveri steam turbines, which produced 110 MW to the shafts.
so 110MW for 30,1 knots, that means for 47,3 knots you need at least 110*1,57^2=271 MW. this is without the additional wave resistance of higher speeds taken into account, so it might end up even higher. the hull shape, which is designed for an speed between 20 and 25 knots most likely, is also not suitable for these speeds
your propellers will not be able to give that much power to the water so you will have to fit your ship with waterjets or something.
so here we find the first reason why building an all new design is cheaper.
then the guns.
the 38cm guns can no longer be produced in this time. the knowledge to build the barrels is long gone, and for an ship sunk 70 years ago from an defeated country, we no longer have an stack of barrels somewhere like we had for the iowa's when they were reactivated
I fail to see the use of an single phalanx only
all guns use most likely ammunition no longer in production.
operationally, this ship will be less useful then the reactivated iowa, due to the fact that it has no tomahawks on board. the main guns are in this time only useful for shore bombardment. in self defence, the ship cannot keep up with modern missiles, against which it's armour no longer helps. her speed, impressing when she was originally build, is now done as well by missile destroyers.
in terms of radar, its power will be like an torch against an searchlight. to field new radars, and new guns, you will have to reengineer the entire superstructure, and a lot of the hull. to fit an nuclear plant you will have to redesign..... the rest of the hull.
I await your reply in why anything like this would make any sense, the above is in short why I think it is not.
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). Might be wrong though.