Bruce Berndt has claimedhas claimed that all the claims in Ramanujan's "Lost Notebook" have been proved, with a solution to the the final problem being published by Berndt, Li, and Zaharescu in J. London Math. Soc. in 2019. However, I am not sure that this means that all the formulas in Ramanujan's other writings have been proved. If you have not yet tried directly writing to Bruce Berndt, that would be my first suggestion.