Boosting with highly correlated features
Actually, your understanding of a random forest is not 100 percent correct. Variables are sampled per split, not by tree. So every tree has access to all variables.

In general, tree based models are not too strongly affected by highly correlated features. There are no numeric stability issues as with least squares. You can easily add a variable twice without numeric problem. Note however that most interpretability tools like split importance or partial dependence plots are affected by multicollinearity. So be careful with them in such cases.