> DNA testing revealed that I am 47% Jewish

That's not what DNA tests do. They do not tell you whether you are factually X% of A and Y% of B, as they do not have the data to make such claims and they do not have DNA of ones' ancestors except through inference.

What they do tell you is that, based on current day large-scale survey data which they use to identify markers, you share certain markers with certain contemporary groups. Especially the percentages they give you should take with a grain of salt as they are approximations to a ground truth (one which nobody fully knows).