To the best of my knowledge, the Prophet (ﷺ) did not take his meals in a big tray at all, nor did he ever eat well-baked thin bread, nor did he ever eat at a dining table.
Sahih al-Bukhari Book 70, Hadith 14
← Previous Hadith We were in the company of Anas whose baker was with him. Anas said, The Prophet (ﷺ) did not eat thin bread, or a roasted sheep till he met Allah (died).

Sahih al-Bukhari Book 70, Hadith 13 Next Hadith → The Prophet (ﷺ) halted to consummate his marriage with Safiyya. I invited the Muslims to his wedding banquet. He ordered that leather dining sheets be spread. Then dates, dried yoghurt and butter were put on those sheets. Anas added: The Prophet (ﷺ) consummated his marriage with Safiyya (during a journey) whereupon Hais (sweet dish) was served on a leather dining sheet.

Sahih al-Bukhari Book 70, Hadith 15