I would use an area on area overlayer to separate the overlap, then dissolve the overlapping segment back into one of the roads. You will probably need some logic to ensure you dissolve back to the correct road segment.

I tried that way and the result became like this. Is there a way to fill that gap? Could you share the parameters of the transformers used?

This sort of process, with a group by on the dissolve should ensure you have no gap, the tricky bit is to work out so the group by dissolves the overlap into the correct road segment

That gives me this sort of result

from a starting point of this

The parameters in mine are shown like this.And for grouping I dont have the option that you have.