There is no "d" consonant in these words. If a "d" sound is inserted into "cars" it becomes "cards". If someone is referring to a plurality of automobiles, and you're distinctly hearing "cards", that person is making a mistake or has some kind of speech impairment.
Your pronunciation notation appears questionable. Let's look at "cars". It depends on dialect. If you're in Britain, it is /kɑːz/. In the predominant dialect spoken in North America, /ka:rz/.
/seɪz/ is incorrect; that notation follows the pronunciation pattern of "days" /deɪz/. Unlike in "days", in the written form of "says", the letters "ay" do not denote a dipthong; the pronunication is just /sez/.
"Say" is /seɪ/, of course, but the third person inflection is not formed simply by adding /z/.
The "says" part of "essays" is pronounced /seɪz/, but that is not related to "say".
I can hardly think of any other place in the spelling of the language where "ays" goes to /ez/. Other than in "says", it "ay" corresponds to /eɪ/ except in certain words like "papaya" and "picayune" which are of a completely different formation. Let's not forget the troublesome "quay" which sounds exactly like "key" (except to some North Americans). So, good news: "says" may be the only example of its kind that you have to memorize.
There is no word /seɪz/, and if we add a /d/ to make /seɪdz/, that is also not a word; however, there exist surnames Seyds and Seyd.