Is it true that Eid prayers during the time of the Prophet (peace be upon him) were held in the musalla outside the built area because the mosque was not spacious enough, and that if there had been a mosque large enough to accommodate the people, prayer in it would have been better than in any other place?

The practice of the Prophet, peace and blessings be upon him, and his companions was to perform the Eid prayers in the musalla (prayer ground) outside the city, unless there was an excuse. Scholars infer this from the actions of the Prophet, peace and blessings be upon him, and the Caliphs who succeeded him, and from the consensus of Muslims, as there is no report of him, peace and blessings be upon him, performing it in the mosque except for an excuse. Although Imam Al-Shafi'i differed regarding the virtue of praying in the mosque if it could accommodate the people of the town, he saw no harm in praying in the musalla. Ibn Al-Hajj emphasized that performing it in the musalla is a confirmed Sunnah, and that performing it in the mosque is an innovation unless absolutely necessary. This is for the purpose of displaying the rituals of Islam and confirming the command for women to go out and witness the good and the supplication of the Muslims.