Did the Prophet ever entertain himself, or was his life exclusively dedicated to acts of obedience and worship?

The Prophet, peace and blessings be upon him, used to entertain himself. His entire life was dedicated to Allah Almighty, including his leisure time. Several hadiths attest to this:

It is narrated from Jabir ibn Samurah, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, would not leave his prayer rug until the sun rose. The Companions would converse and laugh about matters of Jahiliyyah (pre-Islamic ignorance) and poetry, and the Prophet, peace and blessings be upon him, would smile and laugh with them.

It is narrated from Abu Hurairah, may Allah be pleased with him, that the Companions said, "O Messenger of Allah, you joke with us." He replied, "Indeed, I only speak the truth."

It is narrated from Ya'la ibn Murrah, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, played with and kissed Al-Husain, may Allah be pleased with him.

It is narrated from Anas ibn Malik, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, joked with a man named Zahir ibn Haram by embracing him from behind while he was selling his goods, and said, "Who will buy this slave?" And he said to him, "You are not worthless in the sight of Allah."

It is narrated from Aishah, may Allah be pleased with her, that the Prophet, peace and blessings be upon him, said, "Let the Jews know that in our religion there is latitude; I have been sent with a tolerant and easy religion."

Imam Al-Tirmidhi dedicated two chapters in his "Shama'il" (characteristics) to the Prophet's laughter and joking. A person may be rewarded for their sleep, play, and playing with their family if they have a good intention, as Mu'adh ibn Jabal, may Allah be pleased with him, said, "As for me, I sleep and I stand [in prayer], and I seek reward for my sleep just as I seek reward for my standing [in prayer]."