There's more to this than simply formality. The meaning of 'provided' and 'providing' is more than simply 'if'. They mean "If AND ONLY IF".

We will let you watch TV if you wash the dishes. We will let you watch TV provided that you wash the dishes. . If you get there quickly you can beat he queue. Provided that you get there quickly you can beat the queue. As Noah commented. Provided that is taken as more formal now.

thank you.Noah

"Provided (that)" means the same thing as "if". "Provided (that)" sound more formal to me. https://dictionary.cambridge.org/dictionary/english/provided-that