What is the ruling on observing voluntary fasting out of joy at the birth of the Prophet (peace and blessings be upon him)? And what is the ruling on regularly fasting on Mondays with the intention of expressing joy and celebrating the birth of the Prophet (peace and blessings be upon him), considering that his noble birth occurred on this day?

The first to fast on Monday out of joy at the birth of the Prophet (peace and blessings be upon him)
he first to fast on Mondays out of joy for his birth was the Prophet (peace and blessings be upon him) himself. Abu Qatadah al-Ansari (may Allah be pleased with him) narrated that when the Prophet (peace and blessings be upon him) was asked about fasting on Mondays, he replied, “That is the day on which I was born” (recorded by Muslim in his Ṣahih). This shows the permissibility of expressing joy at the Prophet’s birth by fasting on the day on which it occurred.  

Voluntary fasting in gratitude for Allah’s blessings
Numerous reports and narrations point to the recommendation of fasting as an expression of joy and gratitude on days of divine favor. Among them is the hadith narrated by Ibn ʿAbbas (may Allah be pleased with them both), who said that the Messenger of Allah (peace and blessings be upon him) came to Medina and found the Jews fasting on the day of ʿAshura`. He asked them, “What is this day that you are fasting?” They replied, “This is a great day on which Allah saved Moses and his people and drowned Pharaoh and his people. Moses fasted it in gratitude, and so we fast it as well.” Thereupon, the Messenger of Allah (peace and blessings be upon him) said, “We have more right and greater claim to Moses than you.” So, he fasted it and commanded that it be observed (Bukhari and Muslim).

The Prophet (peace and blessings be upon him) expressed his joy at the salvation of Moses (peace be upon him) by fasting on that day. Abu Huraira (may Allah be pleased with him) narrated that the Prophet (peace and blessings be upon him) once passed by some Jews who were fasting on the day of ʿAshura` and asked, “What is this fast?” They replied, “This is the day on which Allah saved Moses and the Children of Israel from drowning, and Pharaoh was drowned on it. It is also the day on which the Ark came to rest on Mount al-Judi. Noah and Moses fasted it in gratitude to Allah.” The Prophet (peace and blessings be upon him) said, “I have a greater claim to Moses and more right to fast on this day.” He then commanded his Companions to fast (recorded by Imam Ahmad in Al-Musnad, as well as by Abu al-Shaykh and Ibn Mardawiah).

Conclusion
If celebrating the day of Prophet Noah’s salvation and the day of Prophet Moses’s victory through fasting and acts of devotion is legislated and permissible, then celebrating the birth of the Prophet (peace and blessings be upon him) by fasting on the day of his birth is even more deserving and firmly established.

And Allah Almighty knows best.