Is the phrase "Indeed, He knows what is secret and what is even more hidden" in His, exalted be He, saying: "And if you speak aloud, then indeed, He knows what is secret and what is even more hidden" the apodosis (answer) of the condition, or is it a causal "fa" (particle) for an omitted condition?

What you mentioned, that the meaning becomes: "And if you do not declare the word aloud, He does not know the secret and what is even more hidden," is incorrect. The condition in His Almighty's saying: (And if you declare the word aloud, He knows the secret and what is even more hidden) is linked to His knowledge, glorified be He, of the secret because He knows the secret and what is even more hidden than it. So, it is more appropriate that He knows what is declared aloud. The meaning is that He, glorified be He, does not need the word to be declared aloud because He knows the secret and what is even more hidden. So, the verse's structure is cast in the form of a condition and its consequence to affirm the certainty of knowledge. As for the answer to the condition, it is omitted, and "then indeed He knows the secret and what is even more hidden" stands in place of the omitted answer to the condition; meaning, do not burden yourself, for there is no merit in declaring it aloud. The condition regarding declaring aloud might be specific to the Prophet's (peace be upon him) diligence in reciting the Quran aloud, serving as an instruction to Muslims that declaring aloud and in secret are equal in supplication, and refuting the polytheists' misconception that declaring aloud is closer to Allah's knowledge than speaking in secret.