Praise be to Allah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, who responded as follows, may Allaah preserve him:
“I do not agree with this. It was not the custom of the salaf to announce the death of someone so that the people could pray over him, except in the case of a person of high standing in the society, such as a rich man who gave to benefit people or a scholar, as the people would be interested in knowing about this news.”
And Allaah knows best.