Is the Qudsi Hadith: "O David, if those who have turned their backs on Me knew of My anticipation for them, My gentleness towards them, and My yearning for them to abandon their sins, they would die of longing for Me, and their limbs would be torn apart out of love for Me. O David, this is My will for those who turn away from Me, so how about those who turn towards Me?" authentic, and is there anything similar in meaning to it?

The hadith (definition) mentioned in the question was cited by Al-Ghazali in "Ihya' Ulum al-Din" in the accounts of Dawud (peace be upon him) without a chain of narration (sanad), and it might be from the Isra'iliyyat (tales of Jewish origin). What suffices over it is what came in the Sahihayn (Bukhari and Muslim) from Anas (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "Allah is more delighted with the repentance of His servant when he repents to Him than one of you who was on his camel in a desolate land, and it escaped from him, carrying his food and drink. He despaired of it, so he came to a tree and lay down in its shade, having despaired of his camel. While he was in that state, behold, his camel was standing by him. He took hold of its rein and then, out of extreme joy, said: 'O Allah, You are my servant and I am Your Lord!' He erred due to extreme joy." Similarly, the Qudsi Hadith states: "O son of Adam, were your sins to reach the clouds of the sky and then you sought My forgiveness, I would forgive you, and I would not mind."