Textually, the celebration of birthdays either personal or for other great Prophets of Allah is unfounded and baseless in Islam.

Allah says in the Qur'an: Indeed in the Messenger of Allah (Muhammad SAW) you have a good example to follow for him who hopes in (the Meeting with) Allah and the Last Day and remembers Allah much.
Quran (Surah Al-Ahzab, Verse 21)

And it is imperative to follow the guidance of Allah in all our endeavors.

And I (Allah) created not the jinns and humans except they should worship Me (Alone).
Qur'an 51 vs 56

Any act of worship not traceable to the Prophet and his companions is certainly an innovation (bid'a).

The Prophet (peace and blessings of Allaah be upon him) said he who innovates something in this matter of ours that is not of it will have it rejected. (Agreed upon)

The Prophet (peace and blessings of Allaah be upon him) stated repeatedly that: "Every newly-invented thing is a bid'ah (innovation), every bid'ah is a going astray, and every going astray will be in the Fire." (Reported by al-Nisaa'i in al-Sunan, Salaat al-'Eedayn, Baab kayfa al-Khutbah). Reports with the same meaning were narrated via Jaabir (may Allaah be pleased with him) by Ahmad, via al-'Irbaad ibn Saariyah by Abu Dawud and via Ibn Mas'ood (may Allaah be pleased with him) by Ibn Maajah.

The Prophet (peace and blessings of Allaah be upon him) used to say, when beginning a khutbah (sermon): " The best of speech is the Book of Allaah and the best of guidance is the guidance of Muhammad. The worst of things are those which are newly-invented, and every innovation is a going astray" (reported by Muslim, no. 867)

There's a post which summarises that the date of birth of the Prophet salallahu alayhi wa Salam is unknown. Read more below.
https://www.nairaland.com/4744456/when-prophet-islaam-salallaahu-alayhi

Read more on the origin of birthdays, celebrating Christmas and Maolid.
https://www.nairaland.com/4905611/birthday-christmas-mawlid-celebration-light

Thank you very much.