What is the ruling on frequent doubt regarding the emission of semen during the daytime in Ramadan, and the resulting waswasa (whispers/obsessive thoughts) about the validity of the fast and the necessity of ghusl (ritual bath)?

To get rid of Satan's whispers (waswas), one must completely disregard all satanic thoughts and whispers. Following waswas is an act of obedience to Satan, who is our enemy.

As for fasting, the emission of semen due to contemplation or looking does not invalidate it, according to the more authoritative opinion. Rather, it is invalidated by the emission of semen through direct contact. Therefore, even if semen is emitted from you due to thinking, your fast is valid as long as it was not emitted through direct contact.