Thank you for your time and explanation, which has helped me to understand that I already have a Surface Library installed which means that the issue that I am experiencing might be related to something else.
I have tried to duplicate the Surface Library into the embedded library just to understand if Archicad was using a different path to avail of different libraries. However, it didn't work.
I have attached a few screenshots in case, by looking at my libraries and folders, you can understand what could be the reason behind this inconvenience.
I have tried to have a look at the "Libraries Project" (as per your suggestion, but I cannot see anything that stands out for this issue.
I have also tried to open the BIMcloud Library and I have tried to upload the "Surface Library" in the "Libraries" folder just in case for this specific project, Archicad was using a different path. However, it didn't work.
What I have just noticed is that this issue applies to this specific project which is running through BIMcloud as I am working in a studio environment.
I just would like to highlight also, that everytime I have uploaded the Surface Library to a certain folder I have always restarted Archicad.
I hope that any of my info could be helpful to get at the bottom of this issue.