What should someone do who is afflicted with the delusion of semen exiting daily, especially if they cannot differentiate between semen and normal discharge, and fear praying in a state of major ritual impurity if they ignore their doubt?

The validity or invalidity of an act of worship depends on what the accountable person believes to be true, not on the reality of the matter itself. This is from the mercy of Allah. So, whoever doubts the occurrence of an impurity should not pay attention to their doubt and should act upon the original state, which is purity. Their worship is valid, especially for those afflicted with obsessive whispers (waswas), as turning away from these whispers is the legally required treatment. If you are certain that what came out of you is semen, which necessitates a ghusl (ritual bath), then you must perform ghusl. However, if there is doubt, nothing is required of you; rather, you maintain the original state, which is purity.