'Stumble upon' is never used in a literal sense. 'Stumble', yes. Possibly 'stumble over' or 'stumble on', but never 'upon'. If you stumble upon something you encounter it by chance, so 'come across' or 'run across' are the commonest synonyms. There is also 'happen upon', which is more formal and old-fashioned. The original meaning of 'happen' (and even 'happy') implied random chance/luck.

I think "stumbled upon" sums up both the literal and figurative meanings very well. That being said, I don't think this is used literally very often. For meaning similar to the figurative sense you could say "happened upon," or "came across,"