Extracting encoded features after CatBoost
I don't believe this is possible, CatBoost does target encoding per split, so you end up with different values of encoding at different trees.

Before each split is selected in the tree (see Choosing the tree
structure), categorical features are transformed to numerical. This is
done using various statistics on combinations of categorical features
and combinations of categorical and numerical features.

https://catboost.ai/docs/concepts/algorithm-main-stages_cat-to-numberic.html
However, if you just want to use the CatBoost encoding algorithm. You can use CatBoostEncoder