What way to incorporate sugar into dough for millefeuille is better? Choosing from two alternatives: separating layers of dough with layers of icing sugar and making dough with a solution of sugar. If the latter option is preferable or no less good than the former one, an additional question I have is what the concentration of such a solution has to be.

P. S. Descriptions of the process of production of this French dessert available on the web advice to cover with icing sugar only the outer layers of pastry, but it will not impact its taste at all.
Typically, puff pastry dough is not sweetened. Instead puff pastry desserts generally rely on added ingredients or fillings to provide sweetness, and the pastry is just a flaky base or case.

The simplest example I can think of is a palmier, which is basically just puff pastry and sugar -- the sugar is sprinkled on finished dough, and it is then rolled and baked right away. If left to sit, or if the sugar is incorporated earlier (such as during the pastry folding process), it will end up dissolving into the pastry. The overall sweetness level will be about the same, but there is a loss of texture from the sugar crystals and less caramelizing during baking; the finished product wouldn't really be the same.

In a millefeuille, which has other sweet elements (frosting, custard filling), changing the sweetness of the pastry by adding sugar during folding or to the dough will change the overall taste of the assembled pastry.