You are trying to compare apples and oranges with my post which you’ve quoted with yours. To help put things in context, that post was a response related to applications with USCIS. Your K1 and potential DV applications are not going through USCIS, they will be going through consular processing. So my statement of “Upon approval, the second application gets cancelled” is not applicable in your case - that was in the context of cases with USCIS.
Like I already responded to your initial PM, based on your scenario, you can also have both your K1 and DV based immigrant applications in the system at the same time. For CP, the second application only gets canceled if you do not show up for your appointment (assuming the first one (whichever got processed first) already got approved). Since you cannot be issued with two visas simultaneously, if you do show up for the second appointment, the first visa which already got issued will then be canceled without prejudice in order for the second visa to get issued.