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I will constrain my answer to the second turning of the wheel of dharma - which is held to be of definitive meaning while the first and third are said to be of interpretive meaning - and answer from Nagarjuna's seminal Fundamental Verses for explaining the Prajñāpāramitā the Buddha's teachings from the Second Turning of the Wheel of Dharma.
This exact question is brought up in Chapter 22, verse 13 and page 448-451 of Tsongkhapa's, Ocean of Reasoning: A Great Commentary on Nagarjuna's Mulamadhyamakakarika:
The following explanation is given:
Just in case you think the story is different for the Buddha and sentient beings we have:
To put a very fine point on it, the topic is brought up again in the Chapter on Nirvana, page 529:
The pithy answer is that the Tathagata continues in the same essenceless existence after his passing away as he did before he passed away and this is similarly true of all sentient beings. We all exist free of essence.
Hope this is helpful!