Maybe I’m missing something but the x and y limit switches don’t seem to do anything. The X carriage hits the idler on the y plate before the x switch engages. The y switch just kind of hangs in the air to the side of the end plate. See the pictures.
It’s hard to tell from your picture but I think you are just missing the t-nut and the screw that the limit switch hits. Here are 3 pictures from our machine on the Z,Y, and X in that order. On the Z the limit switch touches off on the mount for your spindle.