As for the ḥadiths:

Yaʿqūb ibn Sufyān said:
“Abū al-ʿAbbās Ḥaywah ibn Shurayḥ related to me; Baqiyyah narrated to us, from al-Zubaydī, from al-Zuhrī, from Muḥammad ibn ʿAbd Allāh ibn ʿAbbās, who said:

Ibn ʿAbbās used to tell that Allah sent to His Prophet an angel accompanied by Gabriel. The angel said to the Messenger of Allah ﷺ (1):
‘Allah gives you the choice: will you be a servant-prophet, or a king-prophet?’

The Messenger of Allah turned to Gabriel, as though asking his counsel; Gabriel gestured to him to choose humility. The Messenger of Allah ﷺ replied:
‘Rather, I will be a servant-prophet.’

After uttering that sentence, he never again ate a meal while reclining until he met Allah, Exalted is He.

Al-Bukhārī likewise narrated it in al-Tārīkh (2) from Ḥaywah ibn Shurayḥ, and al-Nasāʾī (3) recorded it from ʿAmr ibn ʿUthmān—both of them through Baqiyyah ibn al-Walīd with this chain. The core of the report appears in the Ṣaḥīḥ with wording close to this.

Imām Aḥmad (4) said: ‘Muḥammad ibn Fuḍayl narrated to us, from ʿUmārah, from Abū Zurʿah—and, as far as I know, he narrated it only from Abū Hurayrah—who said:

Gabriel was sitting with the Messenger of Allah ﷺ when he looked up and saw an angel descending from the sky. Gabriel remarked, “This angel has not come down since the day he was created until this very hour.” When the angel descended he said, “O Muḥammad, your Lord has sent me to you: shall He make you a king-prophet or a servant-messenger?”’ (5)

I found it in the copy of the Musnad in my possession in this abbreviated form (6); it is unique through this route.

It is also authentically reported in the two Ṣaḥīḥs (7), in the narration of Ibn ʿAbbās from ʿUmar ibn al-Khaṭṭāb, concerning the occasion when the Messenger of Allah ﷺ swore to keep away from his wives for a month and withdrew to an upper room. When ʿUmar entered, he found nothing there but a small heap of qarad leaves, a suspended leather bag, and a handful of barley. The Prophet was lying on a mat of palm-fiber that had left marks on his side, and ʿUmar’s eyes filled with tears.

The Prophet ﷺ asked, ‘What is the matter with you?’ I replied, ‘O Messenger of Allah, you are the chosen one of Allah among His creation, yet Chosroes and Caesar are living in the luxury they enjoy!’ He sat up, his face reddening, and said, ‘Are you in doubt, O son of al-Khaṭṭāb?’ Then he added, ‘Those are a people whose good things have been hastened for them in the life of this world.’”