What is the authenticity of the hadith that mentions Abu Hurayrah and some Companions leaving due to hunger, and the Prophet, may Allah bless him and grant him peace, giving them two dates?

The gist of what is mentioned in the hadith is that Abu Hurairah and a group of Companions left their homes due to severe hunger. They came to the Prophet, peace and blessings be upon him, who gave them two dates. Then he asked Abu Hurairah about a date he had kept, and he said it was for his mother. So the Prophet gave him two more dates for his mother.

In a narration by Muslim, the Prophet, peace and blessings be upon him, along with Abu Bakr and Umar, went out due to hunger. They went to a man from the Ansar, who honored them by offering dates, water, and slaughtering a sheep. When they were full and quenched, the Prophet reminded them of Allah’s blessing upon them and that they would be questioned about it on the Day of Resurrection.

The hadith also shows: the poverty and need of the Companions; the permissibility for a person to mention his pain, not as a complaint; the desirability of honoring guests; Abu Hurairah's intense devotion to his mother; the Prophet's honoring him when he learned of his eagerness to be devoted to his mother; the permissibility of hearing and reviewing the speech of a foreign woman when there is a need; and the desirability of promptly offering what is available to a guest.