Correct spelling for the English word "didst addition" is [dˈɪdst ɐdˈɪʃən], [dˈɪdst ɐdˈɪʃən], [d_ˈɪ_d_s_t ɐ_d_ˈɪ_ʃ_ə_n] (IPA phonetic alphabet).
"Didst addition" is not a recognized phrase or a common term, and thus there is no etymology available for it. It may be a combination of different words or a phrase that has not been widely used or documented. If you have any additional context or details, I can try to assist you further.