Does the woman who suffers from obsessive doubts and suspicions about ritual purity (taharah) and the invalidation of her fast due to natural discharges, or due to lustful thoughts that cross her mind, fall under Allah’s saying: "Allah does not burden a soul beyond its capacity" (Quran 2:286)?

Giving in to obsessive thoughts is a disease that afflicts the heart, and one should turn away from them. Your fast is valid. The whisperings of the self and the emission of semen due to thought do not invalidate the fast. Ghusl (ritual bathing) is not obligatory unless you are certain of the emission of semen that necessitates ghusl. The emission of madhy (pre-seminal fluid) does not invalidate the fast.