Ability to copy over column level data types will be introduced as part of “Paste Special” enhancement including all the usual suspects like formulas only, formatting only, column widths, etc.
Unless such specific functions are being used, copy pasting a range of cells will always result in cell properties being localized (e.g. cells copied from a Select/Multi-select column will result in those options applied only at the cell level, when pasting).
In the interim, you can copy over such columns to target area and then edit target column data type to Select. This populates options based on column data. What doesn’t work is that it does not pick the colors already defined on options in individual cells. We will address this as a bug.