Are there some examples of CAT(-1) spaces which are not trees which have disconnected Gromov boundary?
Yes, the free product of any two word hyperbolic groups has disconnected Gromov boundary. For proof see the nice survey of Kapovich-Benakli., section 7.
For sure you can not make it to be manifold without boundary.
You can start with a tree and glue to it many compact pieces applying Reshetnyak gluing theorem.