“”””” > A solid cut by a curve (by boolean diff) could stay a solid.
The shape I obtained after sweeping was not a solid, but a joined surface. Am I still doing something wrong?”””””

Yes, phiros post above is the method to use

Extrude your blue profile up past the zig zag (a solid rectangle you have)

Now using curve of zig zag (still have the curve? Or extract it from current zig zag surface)

Boolean diff zig zag from blue block. Delete top part.