What is the ruling on ritual bathing (ghusl) and acts of worship thereafter, if a Muslim performs ghusl from major ritual impurity and then experiences minor ritual impurity (either certainly or doubtfully) during the ghusl, then repeats the ghusl without performing ablution (wudu) before it, but performs ablution after it?

Ablution (Wudu') is a Sunnah (definition) (recommended practice) in ghusl (definition) for major ritual impurity (janabah (definition)), not a pillar or a condition. Therefore, whoever performs ghusl without wudu', their ghusl is valid, and their prayers thereafter are valid, as long as their wudu' has not been nullified. If one experiences an event (hadath (definition)) during ghusl, only their wudu' is invalidated, not the ghusl itself. It is recommended for them to repeat the wudu' and what has passed of the ghusl. Doubt about the occurrence of an event has no effect, as the default is its non-occurrence until proven with certainty.