Did the Messenger ﷺ give zakat or was he poor?

No, the Prophet ﷺ was poor, ﷺ, and the crescent would pass, then another crescent, then another, and no fire would be lit in the house of the Messenger of Allah.

So 'Urwah ibn al-Zubayr, may Allah be pleased with him, said to his aunt, the Mother of the Believers Aisha: "Aunt, what was your food?" She said: "The two black things, dates and water."

ﷺ, and he would tie a stone, or sometimes two stones, to his stomach.

From hunger ﷺ, so zakat was not obligatory on him, may Allah's prayers and peace be upon him.