>to clarify. I have read it everywhere, including the official forums - that feature normalization is not required when training the decision trees model

All the XGBoost decision tree splits are in form of: [feature] >= [treshold], thus any order preserving normalization/transformation (log, sigmoid, z-scoring, min-max etc) won't have any impact on the results. But if the order is not preserved, creating new transformed features can be beneficial.

Without doing any transformations or changes to the modelling procedure, and training data containing years 2000-2014 and test 2015-2080, the predictions would be something similar to those values in 2014 as you originally suspected. There isn't any hidden built-in magic to do anything about data shift.

One common way to tackle this type of time series problems is to switch to autoregressive (type of) modelling. So, instead of just using raw stock prices directly, use yearly change percentages.