I don't think you'll see 4.0 in vcpkg yet as it's still not stable. After seeing this post I took another look at the github page, as I am interested in getting better results with LSTM, and followed the master branch developer build steps here:
https://github.com/tesseract-ocr/tesseract/wiki/Compiling#develop-tesseract
After installing cppan and cmake and following the steps I was able to build from the generated solution file and get a tesseract dll out with no problems. I haven't tried building and linking with it yet.