I burped and regurgitated a tiny amount of fluid (perhaps stomach bile) into my mouth. My gag reflex made me swallow it almost immediately due to gasping for breath. I’ve been researching this topic and it appears that accidental regurgitation doesn’t invalidate my fast, but I want to ask a more knowledgeable person to be sure.

That is correct. Accidental regurgitation does not invalidate the fast. Deliberate regurgitation does. So your fast was valid.