I would do first a Filters ➤ Map ➤ Displace because of the planks joins, then a Filters ➤ Map ➤ Bump map
Start by making your logo to Layer ➤ Layer to image size as well as your BG, it's very important that layers are at the same size, then
Duplicate your background, then the duplicated background, Colors ➤ Desaturate ➤ Desaturate default are good enough, then select your logo, once logo selected Filters ➤ Map ➤ Displace chose as Aux Input the desaturated background
Once the logo is done, duplicate it, then like the background ➤ make the duplicated logo de-saturated, then Filters ➤ Blur ➤ Gaussian blur (4 or 5 is enough)
now keep visible only the background original (colored) and select it in the layer stack, then go to Filters ➤ Map ➤ Bump map and select as Aux input your desaturated and slightly blured logo
If you want to keep a bit of color of your logo, you can re-activate / visible the logo displaced (which is still in color) and play with the layer blending mode and opacity (example below with Mode "Burn" I did not play with opacity below, but you should)
Start by making your logo to Layer ➤ Layer to image size as well as your BG, it's very important that layers are at the same size, then
Duplicate your background, then the duplicated background, Colors ➤ Desaturate ➤ Desaturate default are good enough, then select your logo, once logo selected Filters ➤ Map ➤ Displace chose as Aux Input the desaturated background
Once the logo is done, duplicate it, then like the background ➤ make the duplicated logo de-saturated, then Filters ➤ Blur ➤ Gaussian blur (4 or 5 is enough)
now keep visible only the background original (colored) and select it in the layer stack, then go to Filters ➤ Map ➤ Bump map and select as Aux input your desaturated and slightly blured logo
If you want to keep a bit of color of your logo, you can re-activate / visible the logo displaced (which is still in color) and play with the layer blending mode and opacity (example below with Mode "Burn" I did not play with opacity below, but you should)