What is the ruling on the fast of one who experienced regurgitation, swallowed it inadvertently, then felt a soapy taste in his mouth after abstaining from food and drink (imsak), and subsequently expelled phlegm?

Your fast for these two days is valid, because the regurgitated food did not settle in your mouth to the extent that you could spit it out, and you did not intentionally induce vomiting. It appears that obsessive whispers (waswas) have taken hold of you, and you must ignore these whispers and not pay attention to them, because giving in to them leads to great evil.