Thanks for pointing out that issue in our readme, you're right there is no BCClient folder, this will be corrected. The readme is referring to the folder contained in the latest .zip release file, current latest release is 5.1.0
We have a couple example projects that use Unreal 5.3 and the brainCloud client compiles with no issues there. I will need some more information to better assist with the issue you're having.
Did you get the brainCloud library from the release .zip file or did you download a copy of the repository?
Can you guide me through the steps you took to get to this issue?