Does seeing excrement in a dream, especially when it recurs and in the presence of other people, indicate Allah's wrath, and how can one know the reason for this wrath?

It is not within our purview to interpret dreams, and we advise you to turn away from these thoughts and whisperings (of Shaytan). You should instead maintain your acts of worship and obedience, be diligent in reciting adhkar (remembrance of Allah), and frequently ask Allah for well-being.