In a Standard Format game I use "Technical Machine: Evolution" and the two Pokemon I choose are both Raichu. Does the game still recognize that Raichu BREAK exists despite it not being legal for play in that format, therefore allowing me to search my deck?
No, since Raichu BREAK is not currently legal in Standard Format you cannot attempt to search for it.
Source: TPCi Rules Team (2024-01-04)