How can I tell if my child feels emotionally safe with me? 

According to Islam, the mercy and compassion that Allah Almighty has provided us are reflected in our responsibility as caregivers. Allah Almighty states in the noble Quran at Surah Al Tawbah (9), Verse 128: ‘Without any doubt, there has come to you (O mankind), the Prophet (Muhammad ﷺ) from amongst yourself; (the thought) of your suffering weighs heavily upon him, he is extremely desirous (for the best) for you, and remains most compassionate and most merciful for the believers.’ The parenting example of the holy Prophet Muhammad ﷺ was rooted in emotional warmth and safety. He allowed children to speak openly, corrected them gently, and made them feel valued. It is recorded in Sahih Muslim, Hadith 2319, that the holy Prophet Muhammad ﷺ stated: ‘He is not one of us who does not show mercy to our young.’ 
A child internalises the feeling that they are emotionally safe, not merely loved but profoundly seen and accepted, when they are continuously shown mercy and respect, especially in the face of misbehaviour or errors.