Why did the attitude of both Omar ibn al-Khattab and Bilal ibn Rabah, may Allah be pleased with them, differ at the time of death, so that Omar was fearful and anxious, while Bilal was joyful and optimistic?

The statements of the Companions and the Salaf upon their death varied according to their circumstances. Some were overcome by fear, others by hope, and some by longing and love. All of this is correct. As for Omar, may Allah be pleased with him, because he was the Commander of the Faithful and bore immense responsibilities, due to his perfect knowledge and his fear of Allah, he did not rely on praise.