To what extent is the message true that speaks of the reason for the omission of the vocative particle (yā) before supplication in the Qur’an, and that this is due to the proximity of Allah Almighty to His servant?

This statement is not entirely accurate. The Holy Quran mentions the phrase "O Lord" (يا رب) in verses such as: "And the Messenger will say, 'O my Lord, indeed my people have taken this Quran as [a thing] abandoned.'" (25:30) and "And [the Prophet's] saying, 'O my Lord, indeed these are a people who do not believe.'" (43:88). Furthermore, "ya" (يا) is used for both close and distant addresses. Examples include Allah's calls to the prophets, such as: "O Noah," and "O Hud," as well as Moses' statement to Pharaoh: "And indeed, I think, O Pharaoh, that you are doomed." (17:102).