Praise be to Allah.
It is not permissible to make lost property announcements in the mosque, because the mosques were not built for that purpose; rather they were built to establish the remembrance of Allah. Muslim (568) narrated that Abu Hurayrah (may Allah be pleased with him) said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever hears a man making a lost property announcement in the mosque, let him say: May Allah not restore it to you, for the mosques were not built for this purpose.”
Muslim (569) also narrated from Buraydah (may Allah be pleased with him) that that a man made a lost property announcement in the mosque, saying: Who has found the red camel? The Prophet (blessings and peace of Allah be upon him) said: “May you not find it. The mosques were only built for that for which they were built.”
Ibn ‘Abd al-Barr ((may Allah have mercy on him) said: Allah, may He be exalted, has stated that the mosques are houses that Allah has ordered to be raised (to be cleaned, and to be honoured), in them His Name is glorified in the mornings and in the afternoons or the evenings,. It is for this purpose that they were built, so it is essential that they be kept free of everything for which they were not built.
End quote from al-Istidhkaar (2/368).
See also the answer to question no. 145198.
Urging people to donate to the mosque, or to give charity to the poor, is something that is prescribed and encouraged, and it comes under the heading of calling people to do good and reminding them of it. So there is nothing wrong with doing that in the mosque, or with the khateeb or preacher drawing attention to it, because it comes under the general heading of goodness to which he is calling people.
The Prophet (blessings and peace of Allah be upon him) urged people to give charity from his minbar, as Muslim (1017) narrated from al-Mundhir ibn Jareer, from his father, who said: We were with the Messenger of Allah (blessings and peace of Allah be upon him) during the early morning when some people came who were barefoot and ill-clothed, wearing striped woollen clothes, with their swords hanging from their necks. Most of them, if not all of them, were from Mudar. The expression of the Messenger of Allah (blessings and peace of Allah be upon him) changed because of what he saw in them of poverty. He went in, then he came out and ordered Bilaal to give the adhaan and iqaamah. He prayed then he addressed (the people) and said: “O mankind! Be dutiful to your Lord, Who created you from a single person (Adam), and from him (Adam) He created his wife [Hawwa (Eve)], and from them both He created many men and women; and fear Allah through Whom you demand (your mutual rights), and (do not cut the relations of) the wombs (kinship). Surely, Allah is Ever an All‑Watcher over you” [al-Nisa’ 4:1] and the verse in al-Hashr: “O you who believe! Fear Allah and keep your duty to Him. And let every person look to what he has sent forth for the morrow” [al-Hashr 59:18]. So people gave dinars, dirhams, clothing, a saa’ of wheat and a saa’ of dates, and even half a date.” Then a man from among the Ansaar brought a money bag which his hands could hardly lift, in fact he could not lift it, and the people came one after another until I saw two piles of food and clothing, and I saw the face of the Messenger of Allah (blessings and peace of Allah be upon him) glistening like gold (because of happiness). The Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever sets a good precedent in Islam will have the reward for that and the reward of those who do it after him, without that detracting from their reward in the slightest. And whoever sets a bad precedent in Islam will bear the burden of sin for that, and the burden of those who do it after him, without that detracting from their burden in the slightest.”
There is nothing wrong with announcing public matters in the mosque, that serve the interests of the Muslims, such as announcing a class or a lecture or a course of study, even if that is going to be held somewhere other than the mosque. There is also nothing wrong with announcing a campaign of vaccination or inoculation for children, because that is of general benefit to the Muslims, and will protect their children from sickness. One of the objectives of sharee‘ah is to preserve people’s physical well-being, and if that is not announced then some of them may miss out and be affected by that sickness by Allah’s leave.
What is not allowed is to announce personal matters or purely worldly matters, such as buying and selling, or making lost property announcements.
See also the answer to question no. 112044.
And Allah knows best.