Complexly assembled part or Complex assembled part?

Short answer, both could work depending on what you want to describe. Though complexly is hard to say so I like "complex assembled part" better.

"Complexly assembled part"

here "complexly" modifies the verb (acting as an adjective) "assembled".

This phrasing implies that the part is made up of many smaller parts, and the assembly of them is complex or difficult or intricate. This doesn't necessarily imply that individual sub-parts are complex themselves. It also doesn't necessarily imply that the final part is complex, but logically it mostly is if its assembly is complex.

"Complex assembled part"

here complex would describe the noun "assembled part" or just "part." In this phrasing the final part itself is definitely complex looking and has been put together from many different parts. But the act of assembly is not necessarily complex (but most likely is).

I think a different word that complex would be a little more descriptive:

"The loudly assembled part" vs. "the loud assembled part"

In the first, it is the assembly that is making noise. In the second, it is the final part that is making noise.

Hope this helps!