I am wondering if the emphatic and pharyngealized sounds of Arabic are the same thing as the letter followed by
/ʕ/. So ðˤ, sˤ, tˤ, and dˤ would be ðʕ, sʕ, tʕ, and dʕ. If it's not the case, can you provide some minimal pairs to show the difference?
The call for minimal pairs is inappropriate, a call for evidence is appropriate. Before giving evidence you gotta say what the evidence is evidence of. The gist of your question is that perhaps, the two-segment sequence composed of /ð+ʕ/ is in all respects interchangeable with the single pharyngealized segment written /ðˁ/. Because of Arabic's root-and-pattern morphology system, we can easily tell the difference between /sˁ, tˁ, dˁ/ which are single consonants occupying one root-C position, and clusters such as /sk, tf, tχ, ðʕ, nħ/ and so on, where the first C is C1 and the second is C2, or where the first C is C2 and the third is C3. /wsˁl/ is the root "arrive", /sʕl/ is "cough". Verbs with only two consonants inflects differently from those with three, and those with three consonants inflect differently from those with four. From the inflectional pattern (CV distribution etc) you can tell that both have 3 consonants. This makes sense only if the roots are as I give them and not e.g. /wsʕl/, /sˁl/. You never separate the pharyngeality of /sˁ/ from /s/, and the surface sequence [sʕ] doesn't sound like [sˁ], not even a little.
The IPA transcription might be mildly misleading. The cluster [kh] is also very different from the uvular fricative [χ], but in many transliteration systems, they would be spelled the same. But they are functionally and phonetically very different. If you have some other sense of "the same" in mind, that might be addressed. I suspect that my argument won't satisfy you, but I don't see how adding a minimal pair would resolve the matter.