Is the death of a female relative who burned herself and whose condition improved in the hospital a day before her death considered a normal death or a suicide, especially given that a perpetual charity and Umrah were performed on her behalf?

Refer this matter to medical professionals. If they determine that she died as a result of the burning, then she is considered to have committed suicide. If she repented before death, Allah accepts her repentance. If she did not repent, then she died having committed one of the major sins. It is hoped that your prayers for her and ongoing charity on her behalf will lighten her burden, for she is under the will of Allah Almighty.