In cycles, you have probably set the settings of the material to Displacement Only. Change it to Bump Only or Displacement and Bump to view it properly in cycles.
EDIT: @BCussi the bump appears at my end: https://i.sstatic.net/Y7581.jpg You just have to zoom in a little, the denoising blurs it out at such a distance. Your image texture is not on my computer, so I can't see the colouring properly, but yeah, it's okay. Try giving it a render and also increase the strength of your displacement if you want, and instead of a distance of 0.005 on the bump nodes, try 0.01 or 0.05. And it also looks like you have plugged the bump node into the height of the other bump node and the wave texture into the strength of that bump node, connect THE NORMAL OF THE Bump Node to the normal input of the next bump node, and the wave texture into the height, not the strength like this: In Eevee, it appears okay because Eevee automatically tries to guess what it will look like. Cycles however, is more realistic, that is why it uses everything according to real life values.