Is it obligatory to repeat the ritual bath (ghusl) and change clothes, given the doubt about the transfer of impurity (najāsa) from a blanket to the bedding, and the questioner's having slept on a pillow that has traces of blood from the gums?

The cure for obsessive thoughts (waswas) is to ignore and disregard them. Impurity is not transferred by mere doubt; the default is that it is not transferred. A small amount of impurity is excused. If impurity affects a part of the body, only the contaminated area needs to be washed, and a full ritual bath (ghusl (definition)) is not required. If impurity affects clothing, it is sufficient to wash the affected spot on the garment. All of this applies if you are absolutely certain that impurity has afflicted the body or clothing. However, with doubt, the default is purity. Nothing is required of the questioner in the two scenarios mentioned, and her prayer is valid.