Is bringing a child who was found and announcing him in the mosque so that his family may recognize him considered part of the forbidden "proclamation of lost property"?

There is no harm in announcing a lost child in the mosque, because it is not among the forbidden announcements of lost property. Lost property (ḍāllah) refers to what is found without a protected enclosure, such as camels, cattle, and sheep, and it does not apply to humans. The wisdom behind forbidding the announcement of lost property and selling in the mosque is to diminish and debase worldly matters. This applies to wealth, but preserving souls is a much greater matter. It is permissible to use loudspeakers for this purpose outside of prayer times.